| Some definitions of interest. |
|
comment | Def Kind of comment: $kind == a |
|
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 |
|
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 |
|
surjection_type | Def A onto B == {f:(A![](FONT/dash.png) B)| Surj(A; B; f) } |
| | Thm* A,B:Type. A onto B Type |
|
surject | Def Surj(A; B; f) == b:B. a:A. f(a) = b |
| | Thm* A,B:Type, f:(A![](FONT/dash.png) B). Surj(A; B; f) Prop |