12 lines
461 B
Text
12 lines
461 B
Text
def top := ∀ p : Prop, p → p
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def pext := ∀ (A B : Prop), A → B → A = B
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def supercast (h : pext) (A B : Prop) (a : A) (b : B) : B
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:= @cast A B (h A B a b) a
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def omega : pext → top :=
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λ h A a => supercast h (top → top) A
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(λ z: top => z (top → top) (λ x => x) z) a
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def Omega : pext → top :=
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λ h => omega h (top → top) (λ x => x) (omega h)
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def Omega' : pext → top := λ h => (λ p x => x)
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theorem loopy : Omega = Omega' := rfl
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