| Some definitions of interest. |
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compose | Def (f o g)(x) == f(g(x)) |
| | Thm* A,B,C:Type, f:(B![](FONT/dash.png) C), g:(A![](FONT/dash.png) B). f o g A![](FONT/dash.png) C |
| | Thm* A,B,C:Type, f:(B inj C), g:(A inj B). f o g A inj C |
| | Thm* f:(B onto C), g:(A onto B). f o g A onto C |
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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 |