Who Cites dequiv? | |
dequiv | Def DecidableEquiv == T:TypeE:TTEquivRel(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:(TTProp). (EquivRel x,y:T. E(x,y)) Prop | |
pi1 | Def 1of(t) == t.1 |
Thm* A:Type, B:(AType), p:(a:AB(a)). 1of(p) A | |
top | Def Top == Void given Void |
Thm* Top Type | |
pi2 | Def 2of(t) == t.2 |
Thm* A:Type, B:(AType), p:(a:AB(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:(TTProp). 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:(TTProp). 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:(TTProp). Refl(T;x,y.E(x,y)) Prop |
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