| Who Cites dequiv? |
|
dequiv |
Def DecidableEquiv == T:Type E:T T   EquivRel(T)( (_1 E _2)) Top |
| | Thm* DecidableEquiv Type{i'} |
|
assert |
Def b == if b True else False fi |
| | Thm* b: . b Prop |
|
carrier |
Def |S| == 1of(S) |
| | Thm* S:Structure. |S| Type |
|
eq_dequiv |
Def =(DE) == 1of(2of(DE)) |
| | Thm* E:DecidableEquiv. =(E) |E| |E|   |
|
equiv_rel |
Def EquivRel x,y:T. E(x;y)
== Refl(T;x,y.E(x;y)) & Sym x,y:T. E(x;y) & Trans x,y:T. E(x;y) |
| | Thm* T:Type, E:(T T Prop). (EquivRel x,y:T. E(x,y)) Prop |
|
pi1 |
Def 1of(t) == t.1 |
| | Thm* A:Type, B:(A Type), p:(a:A B(a)). 1of(p) A |
|
top |
Def Top == Void given Void |
| |
Thm* Top Type |
|
pi2 |
Def 2of(t) == t.2 |
| |
Thm* A:Type, B:(A Type), p:(a:A B(a)). 2of(p) B(1of(p)) |
|
trans |
Def Trans x,y:T. E(x;y) == a,b,c:T. E(a;b)  E(b;c)  E(a;c) |
| | Thm* T:Type, E:(T T Prop). Trans x,y:T. E(x,y) Prop |
|
sym |
Def Sym x,y:T. E(x;y) == a,b:T. E(a;b)  E(b;a) |
| | Thm* T:Type, E:(T T Prop). Sym x,y:T. E(x,y) Prop |
|
refl |
Def Refl(T;x,y.E(x;y)) == a:T. E(a;a) |
| | Thm* T:Type, E:(T T Prop). Refl(T;x,y.E(x,y)) Prop |