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@@ -1,30 +0,0 @@ -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.
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