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Diff — Propositional logic

Revision #3049 → #3555 · back to history

modifiedBivalence, noncontradiction, excluded middlefa531303995d
FieldFrom #3049To #3555
mathlib.declClassical.em
mathlib.match_kindspecial_case
mathlib.moduleMathlib.Logic.Basic
noteExcluded middle (`Classical.em`) and noncontradiction are Lean-core theorems, not a Mathlib characterization of classical logic's distinctive features.Excluded middle is `Classical.em` (Lean core, re-exported through Mathlib) and noncontradiction is `not_and_self`; these are theorems but not a Mathlib characterization of classical logic's distinctive features.
provenanceaiai-moderated
statusnot_formalizedpartial
modifiedNumber of distinct interpretationse7d5e6108cca
FieldFrom #3049To #3555
mathlib.declFintype.card_fun
mathlib.match_kindgeneralization
mathlib.moduleMathlib.Data.Fintype.BigOperators
noteThe count 2^n of interpretations is a cardinality fact (`card (Fin n → Bool)`) but is not stated about propositional interpretations.The count 2^n of interpretations follows from `Fintype.card_fun` (giving `card (Fin n → Bool) = 2^n`), but it is not stated about propositional interpretations.
provenanceaiai-moderated
statusnot_formalizedpartial
modifiedUncountably many interpretationsb616373a0b2f
FieldFrom #3049To #3555
mathlib.declCardinal.cantor
mathlib.match_kindgeneralization
mathlib.moduleMathlib.SetTheory.Cardinal.Order
noteUncountability of `ℕ → Bool` follows from Cantor's theorem in Mathlib, but is not stated about propositional interpretations.Uncountability of `ℕ → Bool` follows from Cantor's theorem (`Cardinal.cantor`) in Mathlib, but is not stated about propositional interpretations.
provenanceaiai-moderated
statusnot_formalizedpartial
modifiedEquivalence/biconditional truth condition8bca82d368d8
FieldFrom #3049To #3555
mathlib.moduleMathlib.Logic.BasicInit.Core
addedPrinciple of bivalence and law of excluded middlea715ad04c114
addedInterdefinability of ∨ via ¬ and ∧a90ddb0bc0bf
addedTruth of negation (¬ semantics)660bb6beb891
addedDe Morgan's lawsed46955a3ce1
addedDouble negation985a50e62f11
addedTransposition (contrapositive)bff512f29491
addedMaterial implicationf7855a15422c
addedCommutativity of ∧ and ∨13b85341e6b8
addedAssociativity of ∧ and ∨6cc5634b52c8
addedDistributivity of ∧ over ∨be82f40ef17c
addedExportation14316a195d67
addedDisjunctive syllogism2dab1e6b0fea
addedModus tollens1fcf38af50c7