35 lines
983 B
Text
35 lines
983 B
Text
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Set: pp::colors
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Set: pp::unicode
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Set: pp::colors
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Defined: TypeM
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Defined: TypeU
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Assumed: CastEq
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λ (A A' : TypeM) (a : A) (b : A') (L2 : A' == A), let b' : A := cast L2 b, L3 : b == b' := CastEq L2 b in L3 :
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Π (A A' : TypeM) (a : A) (b : A') (L2 : A' == A), b == cast L2 b
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λ (A A' : TypeM)
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(B : A → TypeM)
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(B' : A' → TypeM)
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(f : Π x : A, B x)
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(g : Π x : A', B' x)
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(a : A)
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(b : A')
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(H1 : (Π x : A, B x) == (Π 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' := TransExt H3 L3,
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L5 : f a == f b' := Congr2 f L4
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in L5 :
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Π (A A' : TypeM)
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(B : A → TypeM)
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(B' : A' → TypeM)
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(f : Π x : A, B x)
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(g : Π x : A', B' x)
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(a : A)
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(b : A')
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(H1 : (Π x : A, B x) == (Π x : A', B' x)),
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f == g → a == b → f a == f (Cast A' A (Symm (DomInj H1)) b)
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