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