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authorLandon D. C. Elkind2021-02-03 16:10:08 -0700
committerLandon D. C. Elkind2021-02-03 16:10:08 -0700
commita32839d6c14a7d9e689e52dfe321091c8fafb517 (patch)
treecb1e8c3a358f78d26491023761fe5bdd3e58a44b /No1.v
parentcbf59b2290f89979e500faacaccaa4d171469c37 (diff)
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-Require Import Unicode.Utf8.
-
-Module No1.
-
-Import Unicode.Utf8. (*We first give the axioms of Principia for the propositional calculus in *1.*)
-
-Axiom MP1_1 : ∀ P Q : Prop,
- (P → Q) → P → Q. (*Modus ponens*)
-
- (**1.11 ommitted: it is MP for propositions containing variables. Likewise, ommitted the well-formedness rules 1.7, 1.71, 1.72*)
-
-Axiom Taut1_2 : ∀ P : Prop,
- P ∨ P→ P. (*Tautology*)
-
-Axiom Add1_3 : ∀ P Q : Prop,
- Q → P ∨ Q. (*Addition*)
-
-Axiom Perm1_4 : ∀ P Q : Prop,
- P ∨ Q → Q ∨ P. (*Permutation*)
-
-Axiom Assoc1_5 : ∀ P Q R : Prop,
- P ∨ (Q ∨ R) → Q ∨ (P ∨ R).
-
-Axiom Sum1_6: ∀ P Q R : Prop,
- (Q → R) → (P ∨ Q → P ∨ R). (*These are all the propositional axioms of Principia Mathematica.*)
-
-Axiom Impl1_01 : ∀ P Q : Prop,
- (P → Q) = (~P ∨ Q). (*This is a definition in Principia: there → is a defined sign and ∨, ~ are primitive ones. So we will use this axiom to switch between disjunction and implication.*)
-
-End No1. \ No newline at end of file