Index

A

AbelianGroup (class in pylogic.structures.grouplike.group) Abs (class in pylogic.expressions.abs) absolute_value_nonnegative_f() (in module pylogic.proposition.ordering.theorems) Add (class in pylogic.expressions.expr) add() (in module pylogic.expressions.expr) add_negative_to_left() (pylogic.proposition.ordering.lessorequal.LessOrEqual method) add_negative_to_right() (pylogic.proposition.ordering.greaterorequal.GreaterOrEqual method) add_nonnegative_to_left() (pylogic.proposition.ordering.greaterorequal.GreaterOrEqual method) (pylogic.proposition.ordering.greaterthan.GreaterThan method) add_nonnegative_to_right() (pylogic.proposition.ordering.lessorequal.LessOrEqual method) (pylogic.proposition.ordering.lessthan.LessThan method) add_nonpositive_to_left() (pylogic.proposition.ordering.lessorequal.LessOrEqual method) (pylogic.proposition.ordering.lessthan.LessThan method) add_nonpositive_to_right() (pylogic.proposition.ordering.greaterorequal.GreaterOrEqual method) (pylogic.proposition.ordering.greaterthan.GreaterThan method) add_positive_gt_parts() (in module pylogic.theories.numbers) add_positive_to_left() (pylogic.proposition.ordering.greaterorequal.GreaterOrEqual method) add_positive_to_right() (pylogic.proposition.ordering.lessorequal.LessOrEqual method) add_to_both_sides_of_inequality (pylogic.structures.ordered_set.OrderedSet attribute) all_proven() (pylogic.proposition.and_.And method) And (class in pylogic.proposition.and_) and_() (pylogic.proposition.proposition.Proposition method) and_reverse() (pylogic.proposition.proposition.Proposition method) apply() (pylogic.proposition.relation.equals.Equals method) are_negs() (in module pylogic.proposition.not_)

args (pylogic.proposition.proposition.Proposition attribute) arguments (pylogic.proposition.and_.InferenceRule attribute) (pylogic.proposition.contradiction.InferenceRule attribute) (pylogic.proposition.exor.InferenceRule attribute) (pylogic.proposition.iff.InferenceRule attribute) (pylogic.proposition.implies.InferenceRule attribute) (pylogic.proposition.not_.InferenceRule attribute) (pylogic.proposition.or_.InferenceRule attribute) (pylogic.proposition.proposition.InferenceRule attribute) (pylogic.proposition.quantified.exists.InferenceRule attribute) (pylogic.proposition.quantified.forall.InferenceRule attribute) (pylogic.proposition.relation.contains.InferenceRule attribute) (pylogic.proposition.relation.subsets.InferenceRule attribute) arity (pylogic.proposition.proposition.Proposition attribute) as_text() (pylogic.proposition.iff.Iff method) (pylogic.proposition.implies.Implies method) (pylogic.proposition.not_.Not method) (pylogic.proposition.proposition.Proposition method) (pylogic.proposition.relation.relation.Relation method) assume() (in module pylogic.helpers) (pylogic.proposition.proposition.Proposition method) AssumptionsContext (class in pylogic.assumptions_context) atoms (pylogic.expressions.expr.Expr property) (pylogic.proposition.proposition.Proposition property) attr_names (pylogic.structures.grouplike.magma.CustomAttrNamesKwargs attribute) AttrNames (class in pylogic.structures.grouplike.magma)

B

BinaryExpression (class in pylogic.expressions.expr) BinaryRelation (class in pylogic.proposition.relation.binaryrelation) bounded_above() (pylogic.theories.real_numbers.RealsField method) bounded_above_has_lub (pylogic.theories.real_numbers.RealsField attribute) by_call() (in module pylogic.infix.by) by_containment_func() (pylogic.proposition.relation.contains.IsContainedIn method) by_definition() (pylogic.proposition.ordering.lessthan.LessThan method) (pylogic.proposition.relation.contains.IsContainedIn method) by_empty() (pylogic.proposition.relation.subsets.IsSubsetOf method) by_eval() (pylogic.proposition.relation.equals.Equals method) by_forall() (in module pylogic.infix.by) by_inspection() (pylogic.proposition.proposition.Proposition method) (pylogic.proposition.relation.subsets.IsSubsetOf method) by_inspection_check() (pylogic.proposition.not_.Not method) (pylogic.proposition.ordering.greaterorequal.GreaterOrEqual method) (pylogic.proposition.ordering.greaterthan.GreaterThan method) (pylogic.proposition.ordering.lessorequal.LessOrEqual method) (pylogic.proposition.ordering.lessthan.LessThan method) (pylogic.proposition.ordering.partial.PartialOrder method) (pylogic.proposition.ordering.partial.StrictPartialOrder method) (pylogic.proposition.proposition.Proposition method) (pylogic.proposition.relation.binaryrelation.BinaryRelation method) (pylogic.proposition.relation.contains.IsContainedIn method) (pylogic.proposition.relation.divides.Divides method) (pylogic.proposition.relation.equals.Equals method) (pylogic.proposition.relation.subsets.IsSubsetOf method) (pylogic.theories.natural_numbers.Prime method)

by_predicate() (pylogic.proposition.relation.contains.IsContainedIn method) by_simplification() (pylogic.proposition.relation.equals.Equals method) by_single_substitution() (pylogic.proposition.quantified.exists.Exists method) by_substitution() (pylogic.proposition.quantified.exists.Exists method) ByProvers (class in pylogic.infix.by)

C

CalledFunction (class in pylogic.expressions.function) CartesPower (class in pylogic.structures.set_) CartesProduct (class in pylogic.structures.set_) cbrt() (in module pylogic.expressions.expr) Class() (in module pylogic.structures.class_) class_() (in module pylogic.structures.class_) class_n_hash() (in module pylogic.structures.class_) class_n_init() (in module pylogic.structures.class_) class_n_repr() (in module pylogic.structures.class_) close() (pylogic.assumptions_context.AssumptionsContext method) close_all_scopes() (pylogic.proposition.proposition.Proposition method) closed_under_successor (pylogic.theories.natural_numbers.NaturalsSemiring attribute) Collection (class in pylogic.structures.collection) CommutativeRIng (class in pylogic.structures.ringlike.commutative_ring) Complement (class in pylogic.structures.set_) conclude() (in module pylogic.assumptions_context) Constant (class in pylogic.constant) constants() (in module pylogic.constant) containment_function (pylogic.structures.grouplike.magma.CustomAttrNamesKwargs attribute) containment_function() (in module pylogic.structures.class_) (pylogic.structures.grouplike.loop.Loop method) (pylogic.structures.grouplike.magma.Magma method) (pylogic.structures.grouplike.monoid.Monoid method) (pylogic.structures.set_.Set method) (pylogic.variable.Variable method) contains() (in module pylogic.structures.class_) (pylogic.expressions.sequence_term.SequenceTerm method) (pylogic.structures.sequence.Sequence method) (pylogic.structures.set_.Set method) (pylogic.symbol.Symbol method) (pylogic.variable.Variable method) contains_self() (in module pylogic.expressions.function) context_variable() (in module pylogic.assumptions_context) context_variables() (in module pylogic.assumptions_context) Contradiction (class in pylogic.proposition.contradiction)

contradicts() (pylogic.proposition.proposition.Proposition method) contrapositive() (pylogic.proposition.iff.Iff method) (pylogic.proposition.implies.Implies method) converse() (pylogic.proposition.iff.Iff method) copy() (in module pylogic.helpers) (in module pylogic.structures.class_) (pylogic.constant.Constant method) (pylogic.expressions.expr.Expr method) (pylogic.proposition.contradiction.Contradiction method) (pylogic.proposition.iff.Iff method) (pylogic.proposition.implies.Implies method) (pylogic.proposition.not_.Not method) (pylogic.proposition.proposition.Proposition method) (pylogic.proposition.quantified.exists.ExistsInSet method) (pylogic.proposition.quantified.exists.ExistsSubset method) (pylogic.proposition.quantified.exists.ExistsUnique method) (pylogic.proposition.quantified.exists.ExistsUniqueInSet method) (pylogic.proposition.quantified.exists.ExistsUniqueSubset method) (pylogic.proposition.quantified.forall.ForallInSet method) (pylogic.proposition.quantified.forall.ForallSubsets method) (pylogic.proposition.relation.binaryrelation.BinaryRelation method) (pylogic.proposition.relation.divides.Divides method) (pylogic.proposition.relation.relation.Relation method) (pylogic.proposition.relation.subsets.IsSubsetOf method) (pylogic.structures.set_.Set method) (pylogic.symbol.Symbol method) (pylogic.theories.natural_numbers.Prime method) countable() (pylogic.structures.set_.Set method) (pylogic.variable.Variable method) CrookedSemirIng (class in pylogic.structures.ringlike.crooked_semiring) CrookedSemirng (class in pylogic.structures.ringlike.crooked_semirng) ctx_var() (in module pylogic.assumptions_context) ctx_vars() (in module pylogic.assumptions_context) CustomAttrNamesKwargs (class in pylogic.structures.grouplike.magma) CustomExpr (class in pylogic.expressions.expr)

D

de_morgan() (pylogic.proposition.and_.And method) (pylogic.proposition.not_.Not method) (pylogic.proposition.or_.Or method) (pylogic.proposition.proposition.Proposition method) (pylogic.proposition.quantified.exists.Exists method) (pylogic.proposition.quantified.forall.Forall method) deduced_from (pylogic.proposition.proposition.Proposition attribute) deepcopy() (in module pylogic.helpers) (in module pylogic.structures.class_) (pylogic.constant.Constant method) (pylogic.expressions.expr.Expr method) (pylogic.proposition.contradiction.Contradiction method) (pylogic.proposition.iff.Iff method) (pylogic.proposition.implies.Implies method) (pylogic.proposition.not_.Not method) (pylogic.proposition.proposition.Proposition method) (pylogic.proposition.quantified.exists.ExistsInSet method) (pylogic.proposition.quantified.exists.ExistsSubset method) (pylogic.proposition.quantified.exists.ExistsUnique method) (pylogic.proposition.quantified.exists.ExistsUniqueInSet method) (pylogic.proposition.quantified.exists.ExistsUniqueSubset method) (pylogic.proposition.quantified.forall.ForallInSet method) (pylogic.proposition.quantified.forall.ForallSubsets method) (pylogic.proposition.relation.binaryrelation.BinaryRelation method) (pylogic.proposition.relation.divides.Divides method) (pylogic.proposition.relation.relation.Relation method) (pylogic.proposition.relation.subsets.IsSubsetOf method) (pylogic.structures.set_.Set method) (pylogic.symbol.Symbol method) (pylogic.theories.natural_numbers.Prime method)

default_assumptions (pylogic.sympy_helpers.PylSympyExpr attribute) (pylogic.sympy_helpers.PylSympyExprCondPair attribute) (pylogic.sympy_helpers.PylSympySeqBase attribute) (pylogic.sympy_helpers.PylSympySeqFormula attribute) (pylogic.sympy_helpers.PylSympySet attribute) (pylogic.sympy_helpers.PylSympySymbol attribute) define() (pylogic.expressions.function.Function method) define_predicate() (pylogic.structures.sequence.Sequence method) definite_clause_resolve() (pylogic.proposition.implies.Implies method) definition (pylogic.proposition.proposition.Proposition property) (pylogic.proposition.relation.divides.Divides property) (pylogic.theories.natural_numbers.Prime property) describe() (pylogic.proposition.iff.Iff method) (pylogic.proposition.implies.Implies method) (pylogic.proposition.not_.Not method) (pylogic.proposition.proposition.Proposition method) description (pylogic.proposition.proposition.Proposition attribute) Difference (class in pylogic.structures.set_) distance() (in module pylogic.expressions.expr) div() (in module pylogic.expressions.expr) Divides (class in pylogic.proposition.relation.divides) divides() (pylogic.theories.integers.IntegersRing method) (pylogic.theories.natural_numbers.NaturalsSemiring method) DivisionRIng (class in pylogic.structures.ringlike.division_ring) doit() (pylogic.expressions.expr.Expr method) dummy_eq() (pylogic.structures.set_.Set method)

E

element (pylogic.proposition.relation.contains.IsContainedIn property) elements (pylogic.structures.grouplike.magma.CustomAttrNamesKwargs attribute) Equals (class in pylogic.proposition.relation.equals) equals() (in module pylogic.structures.class_) (pylogic.expressions.expr.Expr method) (pylogic.structures.sequence.Sequence method) (pylogic.structures.set_.Set method) (pylogic.symbol.Symbol method) eval_same() (in module pylogic.helpers) (pylogic.expressions.expr.Expr method) (pylogic.proposition.proposition.Proposition method) (pylogic.structures.set_.Set method) (pylogic.symbol.Symbol method) evaluate() (pylogic.expressions.abs.Abs method) (pylogic.expressions.expr.Add method) (pylogic.expressions.expr.CustomExpr method) (pylogic.expressions.expr.Expr method) (pylogic.expressions.expr.Mul method) (pylogic.expressions.expr.Pow method) (pylogic.expressions.function.CalledFunction method) (pylogic.expressions.function.Function method) (pylogic.expressions.function.SelfFunc method) (pylogic.expressions.gcd.Gcd method) (pylogic.expressions.limit.Limit method) (pylogic.expressions.max.Max method) (pylogic.expressions.max.MaxElement method) (pylogic.expressions.min.MinElement method) (pylogic.expressions.mod.Mod method) (pylogic.expressions.piecewise.OtherwiseBranch method) (pylogic.expressions.piecewise.PiecewiseBranch method) (pylogic.expressions.piecewise.PiecewiseExpr method) (pylogic.expressions.sequence_term.SequenceTerm method) (pylogic.proposition.relation.equals.Equals method) (pylogic.structures.sequence.Sequence method) (pylogic.structures.set_.Set method) (pylogic.symbol.Symbol method) (pylogic.theories.real_numbers.Interval method)

even() (pylogic.theories.integers.IntegersRing method) (pylogic.theories.natural_numbers.NaturalsSemiring method) Exists (class in pylogic.proposition.quantified.exists) exists_modus_ponens() (pylogic.proposition.quantified.exists.Exists method) ExistsInSet (class in pylogic.proposition.quantified.exists) ExistsSubset (class in pylogic.proposition.quantified.exists) ExistsUnique (class in pylogic.proposition.quantified.exists) ExistsUniqueInSet (class in pylogic.proposition.quantified.exists) ExistsUniqueSubset (class in pylogic.proposition.quantified.exists) ExOr (class in pylogic.proposition.exor) Exor (in module pylogic.proposition.exor) Expr (class in pylogic.expressions.expr) extract() (pylogic.proposition.and_.And method) (pylogic.proposition.quantified.exists.Exists method) extract_conjuncts() (pylogic.proposition.and_.And method) (pylogic.proposition.quantified.forall.Forall method)

F

Field (class in pylogic.structures.ringlike.field) find_first() (in module pylogic.helpers) FiniteCartesProduct (class in pylogic.structures.set_) FiniteIntersection (class in pylogic.structures.set_) FiniteSequence (class in pylogic.structures.sequence) FiniteSet (class in pylogic.structures.set_) FiniteUnion (class in pylogic.structures.set_) first_second (pylogic.symbol.Symbol property) first_unit_definite_clause_resolve() (pylogic.proposition.implies.Implies method) followed_from() (pylogic.proposition.proposition.Proposition method)

Forall (class in pylogic.proposition.quantified.forall) forall_modus_ponens() (pylogic.proposition.quantified.forall.Forall method) ForallInSet (class in pylogic.proposition.quantified.forall) ForallSubsets (class in pylogic.proposition.quantified.forall) forward_implication() (pylogic.proposition.iff.Iff method) from_assumptions (pylogic.proposition.proposition.Proposition attribute) from_proposition() (pylogic.proposition.quantified.exists.Exists class method) (pylogic.proposition.quantified.exists.ExistsInSet class method) FromSympyError Function (class in pylogic.expressions.function)

G

Gcd (class in pylogic.expressions.gcd) get() (pylogic.proposition.relation.equals.Equals method) get_assumptions() (in module pylogic.proposition.proposition) get_class_ns() (in module pylogic.helpers) get_consts() (in module pylogic.helpers) get_first_proven() (pylogic.assumptions_context.AssumptionsContext method) get_independent_dependencies() (pylogic.symbol.Symbol method) get_prop() (in module pylogic.proposition.proof_search) get_proven() (pylogic.assumptions_context.AssumptionsContext method)

get_sets() (in module pylogic.helpers) get_universe() (in module pylogic.enviroment_settings.set_universe) get_vars() (in module pylogic.helpers) getkey() (in module pylogic.helpers) Getter (class in pylogic.helpers) GreaterOrEqual (class in pylogic.proposition.ordering.greaterorequal) GreaterThan (class in pylogic.proposition.ordering.greaterthan) Group (class in pylogic.structures.grouplike.group) gt_implies_neq() (in module pylogic.theories.numbers)

H

has_as_subproposition() (pylogic.proposition.iff.Iff method) (pylogic.proposition.implies.Implies method) (pylogic.proposition.not_.Not method) (pylogic.proposition.proposition.Proposition method) has_been_proven() (in module pylogic.helpers) has_identity (pylogic.structures.grouplike.loop.Loop attribute) (pylogic.structures.grouplike.monoid.Monoid attribute)

has_lub() (pylogic.theories.real_numbers.RealsField method) have_add_inverses (pylogic.structures.ringlike.nearring.NearrIng attribute) (pylogic.structures.ringlike.ring.RIng attribute) (pylogic.structures.ringlike.rng.Rng attribute) have_inverses (pylogic.structures.grouplike.group.Group attribute) have_mul_inverses (pylogic.structures.ringlike.division_ring.DivisionRIng attribute) hypothetical_syllogism() (pylogic.proposition.implies.Implies method)

I

If() (in module pylogic.syntax_helpers.if_) if_() (in module pylogic.syntax_helpers.if_) Iff (class in pylogic.proposition.iff) iff() (pylogic.proposition.proposition.Proposition method) illegal_occur_check() (in module pylogic.structures.class_) (pylogic.structures.set_.Set method) illegal_occur_check_pred() (in module pylogic.structures.class_) (pylogic.structures.set_.Set method) impl_elim() (pylogic.proposition.implies.Implies method) Implies (class in pylogic.proposition.implies) implies() (pylogic.proposition.proposition.Proposition method) in_particular() (pylogic.proposition.quantified.forall.Forall method) (pylogic.proposition.quantified.forall.ForallInSet method) (pylogic.proposition.quantified.forall.ForallSubsets method) Inference (class in pylogic.inference) inference_rule_search() (in module pylogic.proposition.proof_search) inference_rules() (pylogic.proposition.proposition.Proposition class method) InferenceResult (class in pylogic.proposition.proof_search) InferenceRule (class in pylogic.proposition.and_) (class in pylogic.proposition.contradiction) (class in pylogic.proposition.exor) (class in pylogic.proposition.iff) (class in pylogic.proposition.implies) (class in pylogic.proposition.not_) (class in pylogic.proposition.or_) (class in pylogic.proposition.proposition) (class in pylogic.proposition.quantified.exists) (class in pylogic.proposition.quantified.forall) (class in pylogic.proposition.relation.contains) (class in pylogic.proposition.relation.subsets) Infix (class in pylogic.infix.infix) infix_symbol (pylogic.proposition.ordering.greaterorequal.GreaterOrEqual attribute) (pylogic.proposition.ordering.greaterthan.GreaterThan attribute) (pylogic.proposition.ordering.lessorequal.LessOrEqual attribute) (pylogic.proposition.ordering.lessthan.LessThan attribute) (pylogic.proposition.ordering.partial.PartialOrder attribute) (pylogic.proposition.ordering.partial.StrictPartialOrder attribute) (pylogic.proposition.ordering.total.StrictTotalOrder attribute) (pylogic.proposition.ordering.total.TotalOrder attribute) (pylogic.proposition.relation.binaryrelation.BinaryRelation attribute) (pylogic.proposition.relation.contains.IsContainedIn attribute) (pylogic.proposition.relation.equals.Equals attribute) (pylogic.proposition.relation.subsets.IsSubsetOf attribute) infix_symbol_latex (pylogic.proposition.ordering.greaterorequal.GreaterOrEqual attribute) (pylogic.proposition.ordering.greaterthan.GreaterThan attribute) (pylogic.proposition.ordering.lessorequal.LessOrEqual attribute) (pylogic.proposition.ordering.lessthan.LessThan attribute) (pylogic.proposition.ordering.partial.PartialOrder attribute) (pylogic.proposition.ordering.partial.StrictPartialOrder attribute) (pylogic.proposition.ordering.total.StrictTotalOrder attribute) (pylogic.proposition.ordering.total.TotalOrder attribute) (pylogic.proposition.relation.binaryrelation.BinaryRelation attribute) (pylogic.proposition.relation.contains.IsContainedIn attribute) (pylogic.proposition.relation.equals.Equals attribute) (pylogic.proposition.relation.subsets.IsSubsetOf attribute) InfixOnly (class in pylogic.infix.infix) IntegersRing (class in pylogic.theories.integers) Intersection (class in pylogic.structures.set_) Interval (class in pylogic.theories.real_numbers) IntervalFunc (class in pylogic.theories.real_numbers) InvalidRuleError inverse() (pylogic.proposition.iff.Iff method) is_absolute() (in module pylogic.proposition.ordering.greaterthan) is_antisymmetric (pylogic.proposition.ordering.partial.PartialOrder attribute) (pylogic.proposition.relation.binaryrelation.BinaryRelation attribute) is_assumption (pylogic.proposition.proposition.Proposition attribute) is_asymmetric (pylogic.proposition.ordering.partial.StrictPartialOrder attribute) (pylogic.proposition.relation.binaryrelation.BinaryRelation attribute) is_atomic (pylogic.expressions.expr.Expr attribute) (pylogic.proposition.relation.divides.Divides attribute) (pylogic.structures.sequence.Sequence attribute) (pylogic.structures.set_.CartesPower attribute) (pylogic.structures.set_.CartesProduct attribute) (pylogic.structures.set_.Difference attribute) (pylogic.structures.set_.FiniteCartesProduct attribute) (pylogic.structures.set_.FiniteIntersection attribute) (pylogic.structures.set_.FiniteUnion attribute) (pylogic.structures.set_.Intersection attribute) (pylogic.structures.set_.SeqSet attribute) (pylogic.structures.set_.Set attribute) (pylogic.structures.set_.Union attribute) (pylogic.symbol.Symbol attribute) is_axiom (pylogic.proposition.proposition.Proposition attribute) is_closed_under_op (pylogic.structures.grouplike.magma.AttrNames attribute) (pylogic.structures.grouplike.magma.Magma attribute) is_closed_under_plus (pylogic.structures.ringlike.left_ringoid.LeftRingoid attribute) (pylogic.structures.ringlike.right_ringoid.RightRingoid attribute) (pylogic.structures.ringlike.ringoid.Ringoid attribute) is_closed_under_times (pylogic.structures.ringlike.left_ringoid.LeftRingoid attribute) (pylogic.structures.ringlike.right_ringoid.RightRingoid attribute) (pylogic.structures.ringlike.ringoid.Ringoid attribute) is_commutative (pylogic.sympy_helpers.PylSympySeqBase attribute) (pylogic.sympy_helpers.PylSympySeqFormula attribute) is_connected (pylogic.proposition.ordering.total.StrictTotalOrder attribute) (pylogic.proposition.relation.binaryrelation.BinaryRelation attribute) is_even (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_even_power() (in module pylogic.proposition.ordering.greaterthan) is_finite (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property)

is_in() (pylogic.expressions.expr.Expr method) (pylogic.structures.sequence.Sequence method) (pylogic.symbol.Symbol method) is_integer (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_integer_numeric() (in module pylogic.helpers) is_irreflexive (pylogic.proposition.ordering.partial.StrictPartialOrder attribute) (pylogic.proposition.relation.binaryrelation.BinaryRelation attribute) is_iterable() (in module pylogic.helpers) is_list (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_natural (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_negative (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_nonnegative (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_nonpositive (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_nonzero (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_not_in() (pylogic.expressions.expr.Expr method) (pylogic.structures.sequence.Sequence method) (pylogic.symbol.Symbol method) is_numeric() (in module pylogic.helpers) is_odd (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_one_of() (pylogic.proposition.proposition.Proposition method) is_positive (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_prime() (in module pylogic.helpers) is_proven (pylogic.proposition.proposition.Proposition attribute) (pylogic.proposition.proposition.Proposition property) is_python_numeric() (in module pylogic.helpers) is_python_real_numeric() (in module pylogic.helpers) is_rational (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_rational_power() (in module pylogic.proposition.ordering.greaterthan) is_real (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_reflexive (pylogic.proposition.ordering.partial.PartialOrder attribute) (pylogic.proposition.relation.binaryrelation.BinaryRelation attribute) (pylogic.proposition.relation.equals.Equals attribute) is_sequence (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_set (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) is_special_case_of() (pylogic.proposition.proposition.Proposition method) is_strongly_connected (pylogic.proposition.ordering.total.TotalOrder attribute) (pylogic.proposition.relation.binaryrelation.BinaryRelation attribute) is_subset_of() (pylogic.structures.set_.Set method) (pylogic.symbol.Symbol method) is_symmetric (pylogic.proposition.relation.binaryrelation.BinaryRelation attribute) (pylogic.proposition.relation.equals.Equals attribute) is_transitive (pylogic.proposition.ordering.partial.PartialOrder attribute) (pylogic.proposition.ordering.partial.StrictPartialOrder attribute) (pylogic.proposition.relation.binaryrelation.BinaryRelation attribute) (pylogic.proposition.relation.contains.IsContainedIn attribute) (pylogic.proposition.relation.equals.Equals attribute) (pylogic.proposition.relation.subsets.IsSubsetOf attribute) is_ub() (pylogic.theories.real_numbers.RealsField method) is_zero (pylogic.expressions.expr.Expr property) (pylogic.structures.sequence.Sequence property) (pylogic.structures.set_.SeqSet property) (pylogic.structures.set_.Set property) (pylogic.symbol.Symbol property) IsContainedIn (class in pylogic.proposition.relation.contains) IsSubsetOf (class in pylogic.proposition.relation.subsets)

K

key (pylogic.helpers.Getter attribute) kwargs (pylogic.expressions.expr.Expr attribute) (pylogic.structures.set_.Set attribute) (pylogic.symbol.Symbol attribute)

L

latex() (in module pylogic.helpers) latex_print_order() (in module pylogic.printing.printing) latin_square (pylogic.structures.grouplike.group.Group attribute) (pylogic.structures.grouplike.quasigroup.Quasigroup attribute) LEFT (pylogic.helpers.Side attribute) LeftRingoid (class in pylogic.structures.ringlike.left_ringoid)

LessOrEqual (class in pylogic.proposition.ordering.lessorequal) LessThan (class in pylogic.proposition.ordering.lessthan) level (pylogic.structures.set_.Set attribute) Limit (class in pylogic.expressions.limit) Loop (class in pylogic.structures.grouplike.loop) lt_implies_neq() (in module pylogic.theories.numbers)

M

Magma (class in pylogic.structures.grouplike.magma) make_epsilon_N_definition() (pylogic.expressions.limit.Limit class method) Max (class in pylogic.expressions.max) max() (in module pylogic.expressions.expr) MaxElement (class in pylogic.expressions.max) MinElement (class in pylogic.expressions.min) Mod (class in pylogic.expressions.mod) module pylogic pylogic.abc pylogic.assumptions_context pylogic.constant pylogic.enviroment_settings pylogic.enviroment_settings.set_universe pylogic.enviroment_settings.settings pylogic.expressions pylogic.expressions.abs pylogic.expressions.expr pylogic.expressions.function pylogic.expressions.gcd pylogic.expressions.limit pylogic.expressions.max pylogic.expressions.min pylogic.expressions.mod pylogic.expressions.piecewise pylogic.expressions.prod pylogic.expressions.sequence_term pylogic.expressions.sum pylogic.helpers pylogic.inference pylogic.infix pylogic.infix.by pylogic.infix.infix pylogic.infix.is_ pylogic.printing pylogic.printing.printing pylogic.proposition pylogic.proposition.and_ pylogic.proposition.contradiction pylogic.proposition.exor pylogic.proposition.iff pylogic.proposition.implies pylogic.proposition.not_ pylogic.proposition.or_ pylogic.proposition.ordering pylogic.proposition.ordering.greaterorequal pylogic.proposition.ordering.greaterthan pylogic.proposition.ordering.inference pylogic.proposition.ordering.lessorequal pylogic.proposition.ordering.lessthan pylogic.proposition.ordering.ordering pylogic.proposition.ordering.partial pylogic.proposition.ordering.theorems pylogic.proposition.ordering.total pylogic.proposition.proof_search pylogic.proposition.proposition pylogic.proposition.quantified pylogic.proposition.quantified.exists pylogic.proposition.quantified.forall pylogic.proposition.quantified.quantified pylogic.proposition.relation pylogic.proposition.relation.binaryrelation pylogic.proposition.relation.contains pylogic.proposition.relation.divides pylogic.proposition.relation.equals pylogic.proposition.relation.relation pylogic.proposition.relation.subsets pylogic.structures pylogic.structures.class_ pylogic.structures.collection pylogic.structures.grouplike pylogic.structures.grouplike.group pylogic.structures.grouplike.loop pylogic.structures.grouplike.magma pylogic.structures.grouplike.monoid pylogic.structures.grouplike.quasigroup pylogic.structures.grouplike.semigroup pylogic.structures.ordered_set pylogic.structures.ringlike pylogic.structures.ringlike.commutative_ring pylogic.structures.ringlike.crooked_semiring pylogic.structures.ringlike.crooked_semirng pylogic.structures.ringlike.division_ring pylogic.structures.ringlike.field pylogic.structures.ringlike.left_ringoid pylogic.structures.ringlike.nearring pylogic.structures.ringlike.ordered_field pylogic.structures.ringlike.right_ringoid pylogic.structures.ringlike.ring pylogic.structures.ringlike.ringoid pylogic.structures.ringlike.rng pylogic.structures.ringlike.semiring pylogic.structures.ringlike.semirng pylogic.structures.sequence pylogic.structures.set_ pylogic.symbol pylogic.sympy_helpers pylogic.syntax_helpers pylogic.syntax_helpers.if_ pylogic.theories pylogic.theories.integers pylogic.theories.natural_numbers pylogic.theories.numbers pylogic.theories.rational_numbers pylogic.theories.real_numbers pylogic.typing pylogic.variable pylogic.warn

modus_ponens() (pylogic.proposition.proposition.Proposition method) modus_tollens() (pylogic.proposition.not_.Not method) (pylogic.proposition.proposition.Proposition method) Monoid (class in pylogic.structures.grouplike.monoid) mp() (pylogic.proposition.proposition.Proposition method) mt() (pylogic.proposition.proposition.Proposition method) Mul (class in pylogic.expressions.expr) mul() (in module pylogic.expressions.expr) mul_inverse() (pylogic.proposition.ordering.greaterthan.GreaterThan method) (pylogic.proposition.ordering.lessthan.LessThan method) multiply_by_negative() (pylogic.proposition.ordering.greaterthan.GreaterThan method) (pylogic.proposition.ordering.lessthan.LessThan method) multiply_by_positive() (pylogic.proposition.ordering.greaterthan.GreaterThan method) (pylogic.proposition.ordering.lessthan.LessThan method) mutable_attrs_to_copy (pylogic.expressions.expr.Expr attribute) (pylogic.structures.set_.Set attribute) (pylogic.symbol.Symbol attribute)

N

name (pylogic.proposition.and_.InferenceRule attribute) (pylogic.proposition.contradiction.InferenceRule attribute) (pylogic.proposition.exor.InferenceRule attribute) (pylogic.proposition.iff.InferenceRule attribute) (pylogic.proposition.implies.InferenceRule attribute) (pylogic.proposition.not_.InferenceRule attribute) (pylogic.proposition.or_.InferenceRule attribute) (pylogic.proposition.ordering.greaterorequal.GreaterOrEqual attribute) (pylogic.proposition.ordering.greaterthan.GreaterThan attribute) (pylogic.proposition.ordering.lessorequal.LessOrEqual attribute) (pylogic.proposition.ordering.lessthan.LessThan attribute) (pylogic.proposition.ordering.partial.PartialOrder attribute) (pylogic.proposition.ordering.partial.StrictPartialOrder attribute) (pylogic.proposition.ordering.total.StrictTotalOrder attribute) (pylogic.proposition.ordering.total.TotalOrder attribute) (pylogic.proposition.proposition.InferenceRule attribute) (pylogic.proposition.proposition.Proposition attribute) (pylogic.proposition.quantified.exists.InferenceRule attribute) (pylogic.proposition.quantified.forall.InferenceRule attribute) (pylogic.proposition.relation.binaryrelation.BinaryRelation attribute) (pylogic.proposition.relation.contains.InferenceRule attribute) (pylogic.proposition.relation.contains.IsContainedIn attribute) (pylogic.proposition.relation.equals.Equals attribute) (pylogic.proposition.relation.subsets.InferenceRule attribute) (pylogic.proposition.relation.subsets.IsSubsetOf attribute) (pylogic.structures.grouplike.magma.CustomAttrNamesKwargs attribute) (pylogic.sympy_helpers.PylSympyExpr attribute) (pylogic.sympy_helpers.PylSympySymbol attribute)

Namespace (class in pylogic.helpers) NaturalsSemiring (class in pylogic.theories.natural_numbers) NearrIng (class in pylogic.structures.ringlike.nearring) neg() (in module pylogic.proposition.not_) neq_any_thus_not_in_sequence() (pylogic.proposition.quantified.forall.ForallInSet method) neq_any_thus_not_in_set() (pylogic.proposition.quantified.forall.ForallInSet method) nodes_edges (pylogic.symbol.Symbol property) Not (class in pylogic.proposition.not_) not_() (in module pylogic.proposition.not_)

O

odd() (pylogic.theories.integers.IntegersRing method) (pylogic.theories.natural_numbers.NaturalsSemiring method) one (pylogic.structures.ringlike.crooked_semiring.CrookedSemirIng attribute) (pylogic.structures.ringlike.semiring.SemirIng attribute) one_proven() (pylogic.proposition.exor.ExOr class method) (pylogic.proposition.or_.Or method) one_proven_rem_false() (pylogic.proposition.exor.ExOr method) op (pylogic.structures.grouplike.magma.AttrNames attribute) op_is_associative (pylogic.structures.grouplike.semigroup.Semigroup attribute) op_is_commutative (pylogic.structures.grouplike.group.AbelianGroup attribute) open() (pylogic.assumptions_context.AssumptionsContext method) operate (pylogic.infix.infix.PrefixOnly attribute) (pylogic.infix.infix.SpecialInfix attribute) operation (pylogic.structures.grouplike.magma.AttrNames attribute) (pylogic.structures.grouplike.magma.CustomAttrNamesKwargs attribute)

operation_name (pylogic.structures.grouplike.magma.AttrNames attribute) (pylogic.structures.grouplike.magma.CustomAttrNamesKwargs attribute) operation_symbol (pylogic.structures.grouplike.magma.AttrNames attribute) (pylogic.structures.grouplike.magma.CustomAttrNamesKwargs attribute) Or (class in pylogic.proposition.or_) or_() (pylogic.proposition.proposition.Proposition method) or_reverse() (pylogic.proposition.proposition.Proposition method) order_axiom_bf() (in module pylogic.proposition.ordering.theorems) order_definition (pylogic.structures.ordered_set.OrderedSet attribute) order_is_antisymmetric (pylogic.structures.ordered_set.OrderedSet attribute) order_is_reflexive (pylogic.structures.ordered_set.OrderedSet attribute) order_is_strongly_connected (pylogic.structures.ordered_set.OrderedSet attribute) order_is_transitive (pylogic.structures.ordered_set.OrderedSet attribute) OrderedSet (class in pylogic.structures.ordered_set) otherwise() (in module pylogic.expressions.piecewise) OtherwiseBranch (class in pylogic.expressions.piecewise)

P

p_and() (pylogic.proposition.proposition.Proposition method) p_and_reverse() (pylogic.proposition.proposition.Proposition method) p_multiply_by_negative() (pylogic.proposition.ordering.greaterthan.GreaterThan method) (pylogic.proposition.ordering.lessthan.LessThan method) p_multiply_by_positive() (pylogic.proposition.ordering.greaterthan.GreaterThan method) (pylogic.proposition.ordering.lessthan.LessThan method) p_substitute() (pylogic.proposition.proposition.Proposition method) p_substitute_into() (pylogic.proposition.relation.equals.Equals method) p_to_greater_than() (pylogic.proposition.ordering.lessthan.LessThan method) p_to_less_than() (pylogic.proposition.ordering.greaterthan.GreaterThan method) Pair (class in pylogic.structures.sequence) PartialOrder (class in pylogic.proposition.ordering.partial) PeriodicSequence (class in pylogic.structures.sequence) Piecewise (in module pylogic.expressions.piecewise) PiecewiseBranch (class in pylogic.expressions.piecewise) PiecewiseExpr (class in pylogic.expressions.piecewise) plus_has_identity (pylogic.structures.ringlike.crooked_semirng.CrookedSemirng attribute) plus_is_associative (pylogic.structures.ringlike.crooked_semirng.CrookedSemirng attribute) plus_is_commutative (pylogic.structures.ringlike.semirng.Semirng attribute) plus_latin_square (pylogic.structures.ringlike.nearring.NearrIng attribute) (pylogic.structures.ringlike.ring.RIng attribute) (pylogic.structures.ringlike.rng.Rng attribute) Pow (class in pylogic.expressions.expr) pred() (in module pylogic.proposition.proposition) predecessor (pylogic.theories.integers.IntegersRing attribute) predicate() (in module pylogic.proposition.proposition) (in module pylogic.structures.class_) (pylogic.expressions.sequence_term.SequenceTerm method) (pylogic.structures.sequence.Sequence method) (pylogic.structures.set_.Set method) (pylogic.variable.Variable method) predicates() (in module pylogic.proposition.proposition) preds() (in module pylogic.proposition.proposition) Prefix (class in pylogic.infix.infix) PrefixOnly (class in pylogic.infix.infix) Prime (class in pylogic.theories.natural_numbers) prime() (pylogic.theories.natural_numbers.NaturalsSemiring method) Prod (class in pylogic.expressions.prod) product_of_nonnegatives_is_nonnegative (pylogic.structures.ordered_set.OrderedSet attribute) proof_search() (in module pylogic.proposition.proof_search) proof_search_one() (in module pylogic.proposition.proof_search) prop() (in module pylogic.proposition.proposition) property_add_to_both_sides_of_inequality() (pylogic.structures.ordered_set.OrderedSet class method) property_bounded_above_has_lub() (pylogic.theories.real_numbers.RealsField class method) property_closed_under_successor() (pylogic.theories.natural_numbers.NaturalsSemiring class method) property_has_identity() (pylogic.structures.grouplike.loop.Loop class method) (pylogic.structures.grouplike.monoid.Monoid class method) property_have_add_inverses() (pylogic.structures.ringlike.nearring.NearrIng class method) (pylogic.structures.ringlike.ring.RIng class method) (pylogic.structures.ringlike.rng.Rng class method) property_have_inverses() (pylogic.structures.grouplike.group.Group class method) property_have_mul_inverses() (pylogic.structures.ringlike.division_ring.DivisionRIng class method) property_is_closed_under_op() (pylogic.structures.grouplike.magma.Magma class method) property_latin_square() (pylogic.structures.grouplike.group.Group class method) (pylogic.structures.grouplike.quasigroup.Quasigroup class method) property_op_is_associative() (pylogic.structures.grouplike.semigroup.Semigroup class method) property_op_is_commutative() (pylogic.structures.grouplike.group.AbelianGroup class method) property_order_definition() (pylogic.structures.ordered_set.OrderedSet class method) property_order_is_antisymmetric() (pylogic.structures.ordered_set.OrderedSet class method) property_order_is_reflexive() (pylogic.structures.ordered_set.OrderedSet class method) property_order_is_strongly_connected() (pylogic.structures.ordered_set.OrderedSet class method) property_order_is_transitive() (pylogic.structures.ordered_set.OrderedSet class method) property_plus_has_identity() (pylogic.structures.ringlike.crooked_semirng.CrookedSemirng class method) property_plus_is_associative() (pylogic.structures.ringlike.crooked_semirng.CrookedSemirng class method) property_plus_is_commutative() (pylogic.structures.ringlike.semirng.Semirng class method) property_plus_latin_square() (pylogic.structures.ringlike.nearring.NearrIng class method) (pylogic.structures.ringlike.ring.RIng class method) (pylogic.structures.ringlike.rng.Rng class method) property_product_of_nonnegatives_is_nonnegative() (pylogic.structures.ordered_set.OrderedSet class method) property_strict_order_definition() (pylogic.structures.ordered_set.OrderedSet class method) property_strict_order_is_asymmetric() (pylogic.structures.ordered_set.OrderedSet class method) property_strict_order_is_connected() (pylogic.structures.ordered_set.OrderedSet class method) property_strict_order_is_irreflexive() (pylogic.structures.ordered_set.OrderedSet class method) property_strict_order_is_transitive() (pylogic.structures.ordered_set.OrderedSet class method) property_strong_induction_formal() (pylogic.theories.natural_numbers.NaturalsSemiring class method) property_successor_injective() (pylogic.theories.natural_numbers.NaturalsSemiring class method) property_successor_neq_0() (pylogic.theories.natural_numbers.NaturalsSemiring class method) property_times_dist_over_plus() (pylogic.structures.ringlike.ringoid.Ringoid class method) property_times_has_identity() (pylogic.structures.ringlike.crooked_semiring.CrookedSemirIng class method) (pylogic.structures.ringlike.semiring.SemirIng class method) property_times_is_associative() (pylogic.structures.ringlike.crooked_semirng.CrookedSemirng class method) property_times_is_commutative() (pylogic.structures.ringlike.commutative_ring.CommutativeRIng class method) (pylogic.structures.ringlike.field.Field class method) property_times_latin_square() (pylogic.structures.ringlike.division_ring.DivisionRIng class method) property_times_left_dist_over_plus() (pylogic.structures.ringlike.left_ringoid.LeftRingoid class method) property_times_right_dist_over_plus() (pylogic.structures.ringlike.right_ringoid.RightRingoid class method) property_well_ordering_set() (pylogic.theories.natural_numbers.NaturalsSemiring class method) property_zero_is_min_nat() (pylogic.theories.natural_numbers.NaturalsSemiring class method) property_zero_mul_eq_zero() (pylogic.structures.ringlike.crooked_semirng.CrookedSemirng class method) property_zero_product() (pylogic.structures.ringlike.division_ring.DivisionRIng class method) Proposition (class in pylogic.proposition.proposition) proposition() (in module pylogic.proposition.proposition) propositions() (in module pylogic.proposition.proposition) props() (in module pylogic.proposition.proposition) pylogic module pylogic.abc module pylogic.assumptions_context module pylogic.constant module pylogic.enviroment_settings module pylogic.enviroment_settings.set_universe module pylogic.enviroment_settings.settings module pylogic.expressions module pylogic.expressions.abs module pylogic.expressions.expr module pylogic.expressions.function module pylogic.expressions.gcd module pylogic.expressions.limit module pylogic.expressions.max module pylogic.expressions.min module pylogic.expressions.mod module pylogic.expressions.piecewise module pylogic.expressions.prod module pylogic.expressions.sequence_term module pylogic.expressions.sum module pylogic.helpers module pylogic.inference module pylogic.infix module pylogic.infix.by module pylogic.infix.infix module pylogic.infix.is_ module pylogic.printing module pylogic.printing.printing module pylogic.proposition module

pylogic.proposition.and_ module pylogic.proposition.contradiction module pylogic.proposition.exor module pylogic.proposition.iff module pylogic.proposition.implies module pylogic.proposition.not_ module pylogic.proposition.or_ module pylogic.proposition.ordering module pylogic.proposition.ordering.greaterorequal module pylogic.proposition.ordering.greaterthan module pylogic.proposition.ordering.inference module pylogic.proposition.ordering.lessorequal module pylogic.proposition.ordering.lessthan module pylogic.proposition.ordering.ordering module pylogic.proposition.ordering.partial module pylogic.proposition.ordering.theorems module pylogic.proposition.ordering.total module pylogic.proposition.proof_search module pylogic.proposition.proposition module pylogic.proposition.quantified module pylogic.proposition.quantified.exists module pylogic.proposition.quantified.forall module pylogic.proposition.quantified.quantified module pylogic.proposition.relation module pylogic.proposition.relation.binaryrelation module pylogic.proposition.relation.contains module pylogic.proposition.relation.divides module pylogic.proposition.relation.equals module pylogic.proposition.relation.relation module pylogic.proposition.relation.subsets module pylogic.structures module pylogic.structures.class_ module pylogic.structures.collection module pylogic.structures.grouplike module pylogic.structures.grouplike.group module pylogic.structures.grouplike.loop module pylogic.structures.grouplike.magma module pylogic.structures.grouplike.monoid module pylogic.structures.grouplike.quasigroup module pylogic.structures.grouplike.semigroup module pylogic.structures.ordered_set module pylogic.structures.ringlike module pylogic.structures.ringlike.commutative_ring module pylogic.structures.ringlike.crooked_semiring module pylogic.structures.ringlike.crooked_semirng module pylogic.structures.ringlike.division_ring module pylogic.structures.ringlike.field module pylogic.structures.ringlike.left_ringoid module pylogic.structures.ringlike.nearring module pylogic.structures.ringlike.ordered_field module pylogic.structures.ringlike.right_ringoid module pylogic.structures.ringlike.ring module pylogic.structures.ringlike.ringoid module pylogic.structures.ringlike.rng module pylogic.structures.ringlike.semiring module pylogic.structures.ringlike.semirng module pylogic.structures.sequence module pylogic.structures.set_ module pylogic.symbol module pylogic.sympy_helpers module pylogic.syntax_helpers module pylogic.syntax_helpers.if_ module pylogic.theories module pylogic.theories.integers module pylogic.theories.natural_numbers module pylogic.theories.numbers module pylogic.theories.rational_numbers module pylogic.theories.real_numbers module pylogic.typing module pylogic.variable module pylogic.warn module PylogicInternalWarning PylSympyExpr (class in pylogic.sympy_helpers) PylSympyExprCondPair (class in pylogic.sympy_helpers) PylSympyFunction (class in pylogic.sympy_helpers) PylSympySeqBase (class in pylogic.sympy_helpers) PylSympySeqFormula (class in pylogic.sympy_helpers) PylSympySet (class in pylogic.sympy_helpers) PylSympySymbol (class in pylogic.sympy_helpers) PYTHON_OPS_RETURN_PROPS (pylogic.enviroment_settings.settings.Settings attribute) python_to_pylogic() (in module pylogic.helpers)

Q

Quasigroup (class in pylogic.structures.grouplike.quasigroup)

R

Rational() (in module pylogic.helpers) RationalsField (class in pylogic.theories.rational_numbers) RealsField (class in pylogic.theories.real_numbers) reflexive() (pylogic.proposition.relation.binaryrelation.BinaryRelation class method) Relation (class in pylogic.proposition.relation.relation) remove_duplicates() (pylogic.proposition.and_.And method) (pylogic.proposition.exor.ExOr method) (pylogic.proposition.or_.Or method) replace() (in module pylogic.expressions.expr) (in module pylogic.helpers) (pylogic.expressions.expr.Expr method) (pylogic.proposition.iff.Iff method) (pylogic.proposition.implies.Implies method) (pylogic.proposition.not_.Not method) (pylogic.proposition.proposition.Proposition method) (pylogic.proposition.quantified.exists.ExistsInSet method) (pylogic.proposition.quantified.exists.ExistsSubset method) (pylogic.proposition.quantified.exists.ExistsUnique method) (pylogic.proposition.quantified.exists.ExistsUniqueInSet method) (pylogic.proposition.quantified.exists.ExistsUniqueSubset method) (pylogic.proposition.quantified.forall.Forall method) (pylogic.proposition.quantified.forall.ForallInSet method) (pylogic.proposition.quantified.forall.ForallSubsets method) (pylogic.proposition.relation.binaryrelation.BinaryRelation method) (pylogic.proposition.relation.divides.Divides method) (pylogic.structures.sequence.Sequence method) (pylogic.structures.set_.SeqSet method) (pylogic.structures.set_.Set method) (pylogic.symbol.Symbol method) (pylogic.theories.natural_numbers.Prime method)

replace_self_func() (in module pylogic.expressions.function) reset_universe() (in module pylogic.enviroment_settings.set_universe) reverse_implication() (pylogic.proposition.iff.Iff method) RIGHT (pylogic.helpers.Side attribute) RightRingoid (class in pylogic.structures.ringlike.right_ringoid) RIng (class in pylogic.structures.ringlike.ring) Ringoid (class in pylogic.structures.ringlike.ringoid) RIngoid (in module pylogic.structures.ringlike.ringoid) Rng (class in pylogic.structures.ringlike.rng)

S

self (in module pylogic.expressions.function) SelfFunc (class in pylogic.expressions.function) Semigroup (class in pylogic.structures.grouplike.semigroup) SemirIng (class in pylogic.structures.ringlike.semiring) Semirng (class in pylogic.structures.ringlike.semirng) SeqSet (class in pylogic.structures.set_) Sequence (class in pylogic.structures.sequence) sequences() (in module pylogic.structures.sequence) SequenceTerm (class in pylogic.expressions.sequence_term) Set (class in pylogic.structures.set_) set_desc() (pylogic.proposition.proposition.Proposition method) set_description() (pylogic.proposition.proposition.Proposition method) set_sequence (pylogic.structures.set_.FiniteCartesProduct attribute) set_universe() (in module pylogic.enviroment_settings.set_universe) sets() (in module pylogic.structures.set_) Settings (class in pylogic.enviroment_settings.settings) SHOW_ALL_PARENTHESES (pylogic.enviroment_settings.settings.Settings attribute) SHOW_VARIABLE_DEPS (pylogic.enviroment_settings.settings.Settings attribute) Side (class in pylogic.helpers) size (pylogic.symbol.Symbol property) SpecialInfix (class in pylogic.infix.infix) sqrt() (in module pylogic.expressions.expr) str_print_order() (in module pylogic.printing.printing) strict_order_definition (pylogic.structures.ordered_set.OrderedSet attribute)

strict_order_is_asymmetric (pylogic.structures.ordered_set.OrderedSet attribute) strict_order_is_connected (pylogic.structures.ordered_set.OrderedSet attribute) strict_order_is_irreflexive (pylogic.structures.ordered_set.OrderedSet attribute) strict_order_is_transitive (pylogic.structures.ordered_set.OrderedSet attribute) strict_total_order (pylogic.structures.ordered_set.OrderedSet attribute) StrictPartialOrder (class in pylogic.proposition.ordering.partial) StrictTotalOrder (class in pylogic.proposition.ordering.total) strong_induction() (pylogic.theories.natural_numbers.NaturalsSemiring method) strong_induction_formal (pylogic.theories.natural_numbers.NaturalsSemiring attribute) sub() (in module pylogic.expressions.expr) substitute() (pylogic.proposition.proposition.Proposition method) substitute_into() (pylogic.proposition.relation.equals.Equals method) successor (pylogic.theories.integers.IntegersRing attribute) (pylogic.theories.natural_numbers.NaturalsSemiring attribute) successor_injective (pylogic.theories.natural_numbers.NaturalsSemiring attribute) successor_neq_0 (pylogic.theories.natural_numbers.NaturalsSemiring attribute) Sum (class in pylogic.expressions.sum) Symbol (class in pylogic.symbol) symbols (pylogic.expressions.expr.Expr property) (pylogic.proposition.proposition.Proposition property) symbols() (in module pylogic.symbol) symmetric() (pylogic.proposition.not_.Not method) (pylogic.proposition.relation.binaryrelation.BinaryRelation method) (pylogic.proposition.relation.equals.Equals method) sympy_to_pylogic() (in module pylogic.sympy_helpers)

T

ternary_and() (in module pylogic.helpers) ternary_if_not_none() (in module pylogic.helpers) ternary_not() (in module pylogic.helpers) ternary_or() (in module pylogic.helpers) thus_contained_in_all() (pylogic.proposition.relation.contains.IsContainedIn method) thus_contained_in_at_least_one() (pylogic.proposition.relation.contains.IsContainedIn method) thus_contained_in_b() (pylogic.proposition.relation.contains.IsContainedIn method) thus_forall() (pylogic.proposition.proposition.Proposition method) thus_not_empty() (pylogic.proposition.relation.contains.IsContainedIn method) thus_predicate() (pylogic.proposition.relation.contains.IsContainedIn method) thus_there_exists() (pylogic.proposition.proposition.Proposition method) times_dist_over_plus (pylogic.structures.ringlike.ringoid.Ringoid attribute) times_has_identity (pylogic.structures.ringlike.crooked_semiring.CrookedSemirIng attribute) (pylogic.structures.ringlike.semiring.SemirIng attribute) times_is_associative (pylogic.structures.ringlike.crooked_semirng.CrookedSemirng attribute) times_is_commutative (pylogic.structures.ringlike.commutative_ring.CommutativeRIng attribute) (pylogic.structures.ringlike.field.Field attribute) times_latin_square (pylogic.structures.ringlike.division_ring.DivisionRIng attribute) times_left_dist_over_plus (pylogic.structures.ringlike.left_ringoid.LeftRingoid attribute) times_right_dist_over_plus (pylogic.structures.ringlike.right_ringoid.RightRingoid attribute) to_conjunction() (pylogic.proposition.iff.Iff method) to_decimal() (pylogic.constant.Constant method) to_disjunction() (pylogic.proposition.ordering.greaterorequal.GreaterOrEqual method) (pylogic.proposition.ordering.lessorequal.LessOrEqual method) to_exists() (pylogic.proposition.quantified.exists.ExistsInSet method) (pylogic.proposition.quantified.exists.ExistsSubset method) to_exists_in_set() (pylogic.proposition.quantified.exists.Exists method) (pylogic.proposition.quantified.exists.ExistsInSet method) (pylogic.proposition.relation.divides.Divides method) to_exists_unique() (pylogic.proposition.quantified.exists.Exists method) (pylogic.proposition.quantified.exists.ExistsUnique method) to_exists_unique_in_set() (pylogic.proposition.quantified.exists.Exists method) (pylogic.proposition.quantified.exists.ExistsUniqueInSet method) to_exor() (pylogic.proposition.and_.And method) to_forall() (pylogic.proposition.quantified.forall.ForallInSet method) (pylogic.proposition.quantified.forall.ForallSubsets method) (pylogic.proposition.relation.subsets.IsSubsetOf method) to_fraction() (pylogic.constant.Constant method) to_greater_than() (pylogic.proposition.ordering.lessthan.LessThan method) to_intersection() (pylogic.structures.set_.Difference method) to_less_than() (pylogic.proposition.ordering.greaterthan.GreaterThan method) to_negative_inequality() (pylogic.proposition.ordering.greaterthan.GreaterThan method) (pylogic.proposition.ordering.lessthan.LessThan method)

to_positive_inequality() (pylogic.proposition.ordering.greaterthan.GreaterThan method) (pylogic.proposition.ordering.lessthan.LessThan method) to_prove() (in module pylogic.assumptions_context) to_sympy() (in module pylogic.expressions.expr) (in module pylogic.structures.class_) (pylogic.constant.Constant method) (pylogic.expressions.abs.Abs method) (pylogic.expressions.expr.Add method) (pylogic.expressions.expr.Expr method) (pylogic.expressions.expr.Mul method) (pylogic.expressions.expr.Pow method) (pylogic.expressions.function.CalledFunction method) (pylogic.expressions.function.Function method) (pylogic.expressions.function.SelfFunc method) (pylogic.expressions.mod.Mod method) (pylogic.expressions.piecewise.OtherwiseBranch method) (pylogic.expressions.piecewise.PiecewiseBranch method) (pylogic.expressions.piecewise.PiecewiseExpr method) (pylogic.expressions.prod.Prod method) (pylogic.expressions.sum.Sum method) (pylogic.proposition.and_.And method) (pylogic.proposition.iff.Iff method) (pylogic.proposition.implies.Implies method) (pylogic.proposition.not_.Not method) (pylogic.proposition.or_.Or method) (pylogic.proposition.ordering.partial.PartialOrder method) (pylogic.proposition.ordering.partial.StrictPartialOrder method) (pylogic.proposition.relation.equals.Equals method) (pylogic.structures.sequence.FiniteSequence method) (pylogic.structures.sequence.PeriodicSequence method) (pylogic.structures.sequence.Sequence method) (pylogic.structures.set_.Set method) (pylogic.symbol.Symbol method) todo() (in module pylogic.helpers) (pylogic.proposition.proposition.Proposition method) ToSympyError total_order (pylogic.structures.ordered_set.OrderedSet attribute) TotalOrder (class in pylogic.proposition.ordering.total) transitive() (in module pylogic.proposition.ordering.inference) (pylogic.proposition.relation.binaryrelation.BinaryRelation method) Triple (class in pylogic.structures.sequence) try_except() (in module pylogic.helpers) type_check() (in module pylogic.helpers) type_check_no() (in module pylogic.helpers)

U

unbind() (in module pylogic.variable) (pylogic.variable.Variable method) unify() (in module pylogic.helpers) (pylogic.expressions.expr.Expr method) (pylogic.proposition.implies.Implies method) (pylogic.proposition.not_.Not method) (pylogic.proposition.proposition.Proposition method) Union (class in pylogic.structures.set_) unit_definite_clause_resolve() (pylogic.proposition.implies.Implies method) update_properties() (pylogic.expressions.abs.Abs method) (pylogic.expressions.expr.Add method) (pylogic.expressions.expr.CustomExpr method) (pylogic.expressions.expr.Expr method) (pylogic.expressions.expr.Mul method) (pylogic.expressions.expr.Pow method) (pylogic.expressions.function.CalledFunction method) (pylogic.expressions.function.Function method) (pylogic.expressions.function.SelfFunc method) (pylogic.expressions.gcd.Gcd method) (pylogic.expressions.limit.Limit method) (pylogic.expressions.max.Max method) (pylogic.expressions.max.MaxElement method) (pylogic.expressions.min.MinElement method) (pylogic.expressions.mod.Mod method) (pylogic.expressions.piecewise.OtherwiseBranch method) (pylogic.expressions.piecewise.PiecewiseBranch method) (pylogic.expressions.piecewise.PiecewiseExpr method) (pylogic.expressions.prod.Prod method) (pylogic.expressions.sequence_term.SequenceTerm method) (pylogic.expressions.sum.Sum method)

USE_CLASSICAL_LOGIC (pylogic.enviroment_settings.settings.Settings attribute)

V

value (pylogic.helpers.Getter attribute) Var (in module pylogic.variable) var() (pylogic.assumptions_context.AssumptionsContext method) Variable (class in pylogic.variable)

variable() (pylogic.assumptions_context.AssumptionsContext method) variables() (in module pylogic.variable) (pylogic.assumptions_context.AssumptionsContext method) vars() (pylogic.assumptions_context.AssumptionsContext method)

W

weak_induction() (pylogic.theories.natural_numbers.NaturalsSemiring method)

well_ordering() (pylogic.theories.natural_numbers.NaturalsSemiring method) well_ordering_set (pylogic.theories.natural_numbers.NaturalsSemiring attribute)

X

xor() (pylogic.proposition.proposition.Proposition method)

xor_reverse() (pylogic.proposition.proposition.Proposition method)

Z

zero (pylogic.structures.ringlike.crooked_semirng.CrookedSemirng attribute) zero_abs_is_0() (pylogic.proposition.relation.equals.Equals method)

zero_is_min_nat (pylogic.theories.natural_numbers.NaturalsSemiring attribute) zero_mul_eq_zero (pylogic.structures.ringlike.crooked_semirng.CrookedSemirng attribute) zero_product (pylogic.structures.ringlike.division_ring.DivisionRIng attribute)