Def Dec(P) == P P

Thm* A:Prop. Dec(A) Prop

Thm* T:Type, E:(TTProp). (EquivRel x,y:T. E(x,y)) Prop

Def P Q == (P Q) & (P Q)

Thm* A,B:Prop. (A B) Prop

Def == {i:| 0i }

Thm* Type

Def AB == B < A

Thm* i,j:. ij Prop

Def A == A False

Thm* A:Prop. (A) Prop

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

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

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

Def P Q == Q P

Thm* A,B:Prop. (A B) Prop