Def L-induced Equiv(x,y) == z:A*. L(z @ x) L(z @ y)

Thm* A:Type, L:LangOver(A). L-induced Equiv A*A*Prop

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

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

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

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

Def P Q == Q P

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