| | Some definitions of interest. |
|
| compose | Def (f o g)(x) == f(g(x)) |
| | | Thm*  A,B,C:Type, f:(B  C), g:(AB). f o g  AC |
|
| compose2 | Def (f1,f2) o g(x) == g(x)/x,y. < f1(x),f2(y) > |
| | | Thm* A,B,C,B',C':Type, g:(AB C), f1:(BB'), f2:(CC'). (f1,f2) o g AB'C' |
|
| tidentity | Def Id == Id |
| | | Thm* A:Type. Id AA |
|
| identity | Def Id(x) == x |
| | | Thm* A:Type. Id AA |
|
| iff | Def P   Q == (P  Q) & (P Q) |
| | | Thm* A,B:Prop. (A B) Prop |
|
| pi1 | Def 1of(t) == t.1 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A |
|
| pi2 | Def 2of(t) == t.2 |
| | | Thm* A:Type, B:(AType), p:(a:AB(a)). 2of(p) B(1of(p)) |
