Proof step 1 from proof step-absstep-I5-I6-tau-same (conclusion) (back to tree)

System applied rule normalize

And obtained the following new goals

• Proof step 2:

  ls0.n0 = get_hash(ls0.e, ls0.sz), ls.n0 = get_hash(ls.e, ls.sz), ls0.sz = # gs0.ar, ls.sz = # gs.ar, ls.tid = als.tid, lsf(tid).tid = tid, alsf(tid).tid = tid, I6 = pcstepf(gs, ls, I5, τ), alsf(tid) = als, apc = (ls.b ⊃ retInsert;invInsert), apcf(tid) = apc, gs0 = gstepf(gs, ls, I5, τ), ls0 = lstepf(gs, ls, I5, τ), lsf(tid) = ls, lsf0(tid) = ls0, pcf(tid) = I5, pcf0(tid) = I6, # gs.ar ≠ 0, # gs0.ar ≠ 0, ls.e ≠ ⊥, ls0.e ≠ ⊥, ls0.n < # gs0.ar, ls0.n0 < # gs0.ar, ls.n < # gs.ar, ls.n0 < # gs.ar, SetLInv(ags, als, apc), absset(gs.ar, ags.set), allslotsfull(gs0.ar, ls0.n0, ls0.n, ls0.e, false), allslotsfull(gs.ar, ls.n0, ls.n, ls.e, false), htok(gs0.ar), htok(gs.ar), pre(gs, ls, I5, τ), ¬ ls.b, ¬ ls0.b, ls.b → ¬ als.lb, apc = invMember ∨ apc = invInsert → ls.e = als.le, ∀ 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 ⊦ absset(gs0.ar, ags.set) ∧ ls0.tid = als.tid ∧ apc = invInsert ∧ (apc = invMember ∨ apc = invInsert → ls0.e = als.le)

Rule argument

Additional information

Proof step 2 from proof step-absstep-I5-I6-tau-same (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s) lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic ⊦ gstepf(gs, ls, I5, τ) = gs; (s) ⊦ pre(gs, ls, I5, a) ↔ a = τ; (s) ⊦ pcstepf(gs, ls, I5, a) = (¬ ls.b ⊃ I6;I21); (s) ⊦ lstepf(gs, ls, I5, τ) = ls; (s)