Thm* R:(T T Prop). (Sym x,y:T. x R y)  (Sym x,y:T. x (R^*) y) | [rel_star_symmetric] |
Thm* R:(T T Prop), x,y:T. (x R^*^-1 y)  (x (R^-1^*) y) | [rel_inverse_star] |
Thm* x,y:T, R:(T T Prop). x = y  (x (R^*) y) | [rel_star_weakening] |
Thm* R:(T T Prop), x,y,z:T. (x R y)  (y (R^*) z)  (x (R^*) z) | [rel_star_trans] |
Thm* R:(T T Prop), x,y:T. (x R y)  (x (R^*) y) | [rel_rel_star] |
Thm* E:(T T Prop), x,y:T. EquivRel(T)(_1 E _2)  (x (E^*) y)  (x E y) | [rel_star_of_equiv] |
Thm* R,R2:(T T Prop).
Thm* Trans(T)(R2(_1,_2))
Thm* 
Thm* ( x,y:T. (x R y)  (x R2 y))  ( x,y:T. (x (R^*) y)  (x R2 y) x = y) | [rel_star_closure] |
Thm* P:(T Prop), R:(T T Prop). R preserves P  R^* preserves P | [preserved_by_star] |
Thm* R1,R2:(T T Prop), x,y:T. R1 => R2  (x (R1^*) y)  (x (R2^*) y) | [rel_star_monotonic] |
Thm* R:(T T Prop), x,y,z:T. (x (R^*) y)  (y (R^*) z)  (x (R^*) z) | [rel_star_transitivity] |
Thm* R1,R2:(T T Prop). R1 => R2  R1^* => R2^* | [rel_star_monotone] |