Ltac jmstep_inv :=
  match goal with
  | H : JuicyMachine.start_thread _ _ _ _  |- _ => inversion H
  | H : JuicyMachine.resume_thread _ _ _   |- _ => inversion H
  | H : JuicyMachine.threadStep _ _ _ _ _           |- _ => inversion H
  | H : JuicyMachine.suspend_thread _ _ _ |- _ => inversion H
  | H : JuicyMachine.syncStep _ _ _ _ _ _           |- _ => inversion H
(*  | H : JuicyMachine.threadHalted _                   |- _ => inversion H*)
  | H : JuicyMachine.schedfail _         |- _ => inversion H
  end; try subst.Ltac getThread_inv :=
  match goal with
  | [ H : getThreadC ?i _ _ = _ ,
          H2 : getThreadC ?i _ _ = _ |- _ ] =>
    pose proof (getThreadC_fun _ _ _ _ _ _ _ H H2)
  | [ H : getThreadR ?i _ _ = _ ,
          H2 : getThreadR ?i _ _ = _ |- _ ] =>
    pose proof (getThreadR_fun _ _ _ _ _ _ _ H H2)
  end.Ltac substwith x y := assert (x = y) by apply proof_irr; subst x.

Lemma resource_decay_join_identity b phi phi' e e' : resource_decay b phi phi' -> sepalg.joins phi e -> sepalg.joins phi' e' -> identity e -> identity e' -> e' = age_to (level phi') e.