| Some definitions of interest. |
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iff | Def P ![](FONT/if_big.png) Q == (P ![](FONT/eq.png) Q) & (P ![](FONT/if_big.png) Q) |
| | Thm* A,B:Prop. (A ![](FONT/if_big.png) B) Prop |
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inv_pair | Def A![](FONT/if_med.png) B == {fg:((A![](FONT/dash.png) B) (B![](FONT/dash.png) A))| fg/f,g. InvFuns(A;B;f;g) } |
| | Thm* A,B:Type. A![](FONT/if_med.png) B Type |
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one_one_corr_2 | Def A ~ B == f:(A![](FONT/dash.png) B), g:(B![](FONT/dash.png) A). InvFuns(A;B;f;g) |
| | Thm* A,B:Type. (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) |
| | Thm* f:(A![](FONT/dash.png) B), g:(B![](FONT/dash.png) A). InvFuns(A;B;f;g) Prop |