Definition same_except_cur (m m' : Mem.mem) :=
  Mem.mem_contents m = Mem.mem_contents m' /\
  max_access_at m = max_access_at m' /\
  Mem.nextblock m = Mem.nextblock m'.

Lemma mem_cohere_same_except_cur m m' phi : same_except_cur m m' -> mem_cohere' m phi -> mem_cohere' m' phi.