| Some definitions of interest. |
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one_one_corr_2 | Def A ~ B == f:(A B), g:(B A). InvFuns(A;B;f;g) |
| | Thm* A,B:Type. (A ~ B) Prop |
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one_one_corr_fams | Def (x:A. B(x)) ~ (x':A'. B'(x'))
Def == f:(A A'), g:(A' A), F:(x:A B(x) B'(f(x))), G:(x:A B'(f(x)) B(x)).
Def == InvFuns(A;A';f;g) & ( u:A. InvFuns(B(u);B'(f(u));F(u);G(u))) |
| | Thm* A:Type, A':Type, B:(A Type), B':(A' Type).
Thm* ((x:A. B(x)) ~ (x':A'. B'(x'))) Prop |