proposition: Lemma show_associativity_facts : forall c u v w, composable c u v -> composable c v w -> associativity_facts c u v w.
proof: Proof. ir. cp H; uh H; ee. cp H; uh H; ee. clear H7. uhg. do 4 (wr composable_facts_rw). ee; try am. rwi composable_facts_rw H0; rwi composable_facts_rw H1. uh H0; uh H1; ee. ap show_composable. am. am. rw H20. am. ap show_composable. rwi composable_facts_rw H1; uh H1; ee; am. rwi composable_facts_rw H0; uh H0; ee; am. rwi composable_facts_rw H1; uh H1; ee. rw H12. uh H0; ee. uh H14; ee. am. sy; ap H6. am. uh H0; ee; am. Qed.
imports: Arith universe