le 0 y true le s x 0 false le s x s y le x y eq 0 0 true eq 0 s y false eq s x 0 false eq s x s y eq x y minsort nil nil minsort cons x xs cons min cons x xs minsort rm min cons x xs cons x xs min nil 0 min cons x nil x min cons x cons y xs if1 le x y x y xs if1 true x y xs min cons x xs if1 false x y xs min cons y xs rm x nil nil rm x cons y xs if2 eq x y x y xs if2 true x y xs rm x xs if2 false x y xs cons y rm x xs le 2 0 0 true 0 s 1 false 0 eq 2 minsort 1 nil 0 cons 2 min 1 rm 2 if1 4 if2 4 FULL ./AProVE_09_Inductive/minsort.trs