Proof step 1 from proof step-absstep-M18-idle-retMEMBER-same (conclusion) (back to tree)

System applied rule normalize

And obtained the following new goals

• Proof step 2:

  ls.tid = als.tid, lsf(tid).tid = tid, alsf(tid).tid = tid, alsf(tid) = als, apcf(tid) = apc, gs0 = gstepf(gs, ls, M18, retMEMBER(ls.tid, b)), idle = pcstepf(gs, ls, M18, retMEMBER(ls.tid, b)), ls0 = lstepf(gs, ls, M18, retMEMBER(ls.tid, b)), lsf(tid) = ls, lsf0(tid) = ls0, pcf(tid) = M18, pcf0(tid) = idle, # gs.ar ≠ 0, # gs0.ar ≠ 0, SetLInv(ags, als, apc), absset(gs.ar, ags.set), htok(gs0.ar), htok(gs.ar), pre(gs, ls, M18, retMEMBER(ls.tid, b)), apc = invMember ∨ apc = invInsert → ls.e = als.le, pre(ags, als, apc, ARetMember(ls.tid, b)) → ags0 = gstepf(ags, als, apc, ARetMember(ls.tid, b)) ∧ als0 = lstepf(ags, als, apc, ARetMember(ls.tid, b)) ∧ apc0 = pcstepf(ags, als, apc, ARetMember(ls.tid, b)), ∀ tid0. tid0 ≠ tid → HashsetLInv(gs, lsf(tid0), pcf(tid0)) ∧ SetLInv(ags, alsf(tid0), apcf(tid0)) ∧ labs(gs, lsf(tid0), pcf(tid0), ags, alsf(tid0), apcf(tid0)), ∀ tid0. tid0 ≠ tid → alsf(tid0).tid = tid0, ∀ tid0. tid0 ≠ tid → lsf(tid0).tid = tid0, false ⊦ pre(ags, als, apc, ARetMember(ls.tid, b)) ∧ absset(gs0.ar, ags0.set) ∧ ls0.tid = als0.tid ∧ apc0 = idle ∧ (apc0 = invMember ∨ apc0 = invInsert → ls0.e = als0.le)

Rule argument

Additional information

Proof step 2 from proof step-absstep-M18-idle-retMEMBER-same (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information