| | Some definitions of interest. |
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| inv_funs | Def InvFuns(A; B; f; g) == g o f = Id & f o g = Id |
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| | Thm*  A,B:Type, f:(A  B), g:(BA). InvFuns(A; B; f; g)  Prop |
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| compose | Def (f o g)(x) == f(g(x)) |
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| | Thm* A,B,C:Type, f:(BC), g:(AB). f o g AC |
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| | Thm* A,B,C:Type, f:(B inj C), g:(A inj B). f o g A inj C |
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| | Thm* f:(B onto C), g:(A onto B). f o g A onto C |
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| iff | Def P   Q == (P  Q) & (P Q) |
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| | Thm* A,B:Prop. (A B) Prop |
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| inv_funs_2 | Def InvFuns(A;B;f;g) == (x:A. g(f(x)) = x) & (y:B. f(g(y)) = y) |
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| | Thm* f:(AB), g:(BA). InvFuns(A;B;f;g) Prop |
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| tidentity | Def Id == Id |
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| | Thm* A:Type. Id AA |
