2014-12-01 05:16:01 +00:00
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prelude
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2014-09-17 21:39:05 +00:00
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definition Prop := Type.{0}
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2014-06-25 20:18:32 +00:00
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2014-07-22 16:43:18 +00:00
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definition false := ∀x : Prop, x
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2014-06-25 20:18:32 +00:00
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check false
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2014-07-22 16:43:18 +00:00
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theorem false_elim (C : Prop) (H : false) : C
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2014-06-25 20:18:32 +00:00
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:= H C
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definition eq {A : Type} (a b : A)
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2014-07-22 16:43:18 +00:00
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:= ∀ {P : A → Prop}, P a → P b
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2014-06-25 20:18:32 +00:00
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check eq
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2014-07-01 23:55:41 +00:00
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infix `=`:50 := eq
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2014-06-25 20:18:32 +00:00
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theorem refl {A : Type} (a : A) : a = a
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:= λ P H, H
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2014-07-22 16:43:18 +00:00
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theorem subst {A : Type} {P : A -> Prop} {a b : A} (H1 : a = b) (H2 : P a) : P b
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2014-06-25 20:18:32 +00:00
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:= @H1 P H2
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