Def z@x == z @ x

Thm* A:Type, R:(A*A*Prop). (EquivRel x,y:A*. x R y) (x,y,z:A*. (x R y) ((z @ x) R (z @ y))) (z:A*, y:x,y:A*//(x R y). z@y x,y:A*//(x R y))

Def as @ bs == Case of as; nil bs ; a.as' a.(as' @ bs) (recursive)

Thm* T:Type, as,bs:T*. (as @ bs) T*

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