31 lines
891 B
Text
31 lines
891 B
Text
Import "cast.lean"
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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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(a : A)
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(b : A')
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(L2 : A' == A),
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let b' : A := cast L2 b,
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L3 : b == b' := CastEq L2 b
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in L3
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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 L1 : A == A' := DomInj H1,
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L2 : A' == A := Symm L1,
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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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in L5
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