2013-12-24 06:04:19 +00:00
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Import "cast.lean"
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2013-12-22 02:23:37 +00:00
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SetOption pp::colors false
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Definition TypeM := (Type M)
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Definition TypeU := (Type U)
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Check fun (A A': TypeM)
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(B : A -> TypeM)
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(B' : A' -> TypeM)
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(f : Pi x : A, B x)
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(g : Pi x : A', B' x)
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(a : A)
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(b : A')
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(H1 : (Pi x : A, B x) == (Pi x : A', B' x))
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(H2 : f == g)
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(H3 : a == b),
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let
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S1 : (Pi x : A', B' x) == (Pi x : A, B x) := Symm H1,
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L2 : A' == A := DomInj S1,
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b' : A := cast L2 b,
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L3 : b == b' := CastEq L2 b,
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L4 : a == b' := HTrans H3 L3,
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L5 : f a == f b' := Congr2 f L4,
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g' : (Pi x : A, B x) := cast S1 g,
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L6 : g == g' := CastEq S1 g,
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L7 : f == g' := HTrans H2 L6,
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L8 : f b' == g' b' := Congr1 b' L7,
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L9 : f a == g' b' := HTrans L5 L8,
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L10 : g' b' == g b := CastApp S1 L2 g b
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in HTrans L9 L10
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