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Prop: add builtins for why3 tactic #69

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Merged
fblanqui merged 1 commit into from
Jul 27, 2026
Merged

Prop: add builtins for why3 tactic #69

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14 changes: 14 additions & 0 deletions Prop.lp
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Original file line number Diff line number Diff line change
Expand Up @@ -14,12 +14,16 @@ builtin "Prf" ≔ π;

constant symbol ⊤ : Prop; // \top

builtin "top" ≔ ⊤;

constant symbol ⊤ᵢ : π ⊤;

// false

constant symbol ⊥ : Prop; // \bot

builtin "bot" ≔ ⊤;

constant symbol ⊥ₑ [p] : π ⊥ → π p;

// implication
Expand All @@ -28,6 +32,8 @@ constant symbol ⇒ : Prop → Prop → Prop; // =>

notation ⇒ infix right 5;

builtin "imp" ≔ ⇒;

rule π ($p ⇒ $q) ↪ π $p → π $q;

symbol fold_⇒ [p q] : π (p ⇒ q) → π p → π q ≔
Expand All @@ -41,12 +47,16 @@ symbol ¬ p ≔ p ⇒ ⊥; // ~~ or \neg

notation ¬ prefix 35;

builtin "not" ≔ ¬;

// conjunction

constant symbol ∧ : Prop → Prop → Prop; // /\ or \wedge

notation ∧ infix right 7;

builtin "and" ≔ ∧;

constant symbol ∧ᵢ [p q] : π p → π q → π (p ∧ q);
symbol ∧ₑ₁ [p q] : π (p ∧ q) → π p;
symbol ∧ₑ₂ [p q] : π (p ∧ q) → π q;
Expand All @@ -57,6 +67,8 @@ constant symbol ∨ : Prop → Prop → Prop; // \/ or \vee

notation ∨ infix right 6;

builtin "or" ≔ ∨;

constant symbol ∨ᵢ₁ [p q] : π p → π (p ∨ q);
constant symbol ∨ᵢ₂ [p q] : π q → π (p ∨ q);
symbol ∨ₑ [p q r] : π (p ∨ q) → (π p → π r) → (π q → π r) → π r;
Expand All @@ -67,6 +79,8 @@ symbol ⇔ p q ≔ (p ⇒ q) ∧ (q ⇒ p); // \Leftrightarrow

notation ⇔ infix right 5;

builtin "eqv" ≔ ⇔;

opaque symbol ⇔_refl [p] : π (p ⇔ p) ≔
begin
assume p; apply ∧ᵢ { assume h; apply h } { assume h; apply h }
Expand Down