2014-01-05 20:05:08 +00:00
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variables A B C : (Type U)
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variable P : A -> Bool
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variable F1 : A -> B -> C
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variable F2 : A -> B -> C
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variable H : Pi (a : A) (b : B), (F1 a b) == (F2 a b)
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variable a : A
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check Eta (F2 a)
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check Abst (fun a : A,
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2013-12-16 06:00:26 +00:00
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(Trans (Symm (Eta (F1 a)))
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(Trans (Abst (fun (b : B), H a b))
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(Eta (F2 a)))))
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2014-01-05 20:05:08 +00:00
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check Abst (fun a, (Abst (fun b, H a b)))
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2013-12-16 06:00:26 +00:00
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2014-01-05 20:05:08 +00:00
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theorem T1 : F1 = F2 := Abst (fun a, (Abst (fun b, H a b)))
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theorem T2 : (fun (x1 : A) (x2 : B), F1 x1 x2) = F2 := Abst (fun a, (Abst (fun b, H a b)))
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theorem T3 : F1 = (fun (x1 : A) (x2 : B), F2 x1 x2) := Abst (fun a, (Abst (fun b, H a b)))
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theorem T4 : (fun (x1 : A) (x2 : B), F1 x1 x2) = (fun (x1 : A) (x2 : B), F2 x1 x2) := Abst (fun a, (Abst (fun b, H a b)))
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print environment 4
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setoption pp::implicit true
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print environment 4
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