Notation corestepN := (corestepN (AsmContext.coarse_semantics initU)).

Lemma internal_step_wd: forall tp m tp' m' i (cnti: containsThread tp i) f fg (Hcomp: mem_compatible tp m) (Hmem_wd: valid_mem m) (Hdomain: domain_memren f m) (Htp_wd: tp_wd f tp) (Hge_wd: ge_wd fg the_ge) (Hfg_incr: ren_domain_incr fg f) (Hstep: internal_step cnti Hcomp tp' m'), valid_mem m' /\ (exists f' : memren, ren_domain_incr f f' /\ domain_memren f' m') /\ (forall f' : memren, domain_memren f' m' -> tp_wd f' tp').