lean2/tests/lean/run/e4.lean
Leonardo de Moura 4bc1f3cf81 test(lean/run): add elaborator tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-06-25 16:15:01 -07:00

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definition Bool [inline] := Type.{0}
definition false : Bool := ∀x : Bool, x
check false
theorem false_elim (C : Bool) (H : false) : C
:= H C
definition eq {A : Type} (a b : A)
:= ∀ P : A → Bool, P a → P b
check eq
infix `=` 50 := eq
theorem refl {A : Type} (a : A) : a = a
:= λ P H, H
definition true : Bool
:= false = false
theorem trivial : true
:= refl false
theorem subst {A : Type} {P : A -> Bool} {a b : A} (H1 : a = b) (H2 : P a) : P b
:= H1 _ H2
theorem symm {A : Type} {a b : A} (H : a = b) : b = a
:= subst H (refl a)
theorem trans {A : Type} {a b c : A} (H1 : a = b) (H2 : b = c) : a = c
:= subst H2 H1