diff --git a/prelude/logic.lp b/prelude/logic.lp index d109dc042769173804c04253b27e5a894de9b6e3..101208f76ada5039e23493e680247c58c8fd2aeb 100644 --- a/prelude/logic.lp +++ b/prelude/logic.lp @@ -43,13 +43,9 @@ qed definition xor (a b: η bool) ≔ neq bool a b set flag "print_implicits" on -theorem xor_def: ε (∀ - {bool} - (λa, - ∀ - {bool} - (λb, eq {bool} (xor a b) - (if {bool} a (λ_, ¬ b) (λ_, b))))) +theorem xor_def + : ε (∀ {bool} (λa, ∀ {bool} (λb, eq {bool} (xor a b) + (if {bool} a (λ_, ¬ b) (λ_, b))))) proof admit @@ -83,18 +79,15 @@ definition SETOF ≔ pred constant symbol If_true : ε (∀B - (λt, ∀ - (λx, ∀ {t} (λy, if true (λ_, x) (λ_, y) = x)))) + (λt, ∀ (λx, ∀ {t} (λy, if true (λ_, x) (λ_, y) = x)))) constant symbol If_false : ε (∀B - (λt, ∀ - (λx, ∀ {t} (λy, if false (λ_, x) (λ_, y) = y)))) + (λt, ∀ (λx, ∀ {t} (λy, if false (λ_, x) (λ_, y) = y)))) theorem if_same : ε (∀B (λt, - ∀ {bool} (λb, ∀ (λx: η t, - if b (λ_, x) (λ_, x) = x)))) + ∀ {bool} (λb, ∀ (λx: η t, if b (λ_, x) (λ_, x) = x)))) proof admit @@ -104,12 +97,9 @@ set builtin "refl" ≔ reflexivity_of_equals constant symbol transitivity_of_equals : ε (∀B (λt, - ∀ - (λx: η t, - ∀ - (λy: η t, - ∀ - (λz: η t, (x = y) ∧ (λ_, y = z) ⊃ (λ_, x = z)))))) + ∀(λx: η t, + ∀(λy: η t, + ∀(λz: η t, (x = y) ∧ (λ_, y = z) ⊃ (λ_, x = z)))))) constant symbol symmetry_of_equals