Proof step 1 from proof step-absstep-ready-ready-callFLITCOMPLETE-same (conclusion) (back to tree)

System applied rule normalize

And obtained the following new goals

• Proof step 2:

  ags.ctr = gs.fctr, ags.mem = gs.pmem, gs0.rfo(t) = gs0.bq(t), gs.rfo(t) = gs.bq(t), ls.t = als.t, lsf(t).t = t, alsf(t).t = t, ags.writers = gs.fwriters, alsf(t) = als, apc = ready, apcf(t) = apc, gs0 = gstepf(gs, ls, ready, callFLITCOMPLETE(ls.t)), ls0 = lstepf(gs, ls, ready, callFLITCOMPLETE(ls.t)), lsf(t) = ls, lsf0(t) = ls0, pcf(t) = ready, pcf0(t) = ready, ready = pcstepf(gs, ls, ready, callFLITCOMPLETE(ls.t)), FLITPSCLInv(ags, als, apc), SFTrailing(gs0.bq), SFTrailing(gs.bq), ctrok(ags0.ctr, ags0.writers), ctrok(ags.ctr, ags.writers), ctrok(gs0.fctr, gs0.fwriters), ctrok(gs.fctr, gs.fwriters), noPendingW(t, gs0.bq, gs0.pq), noPendingW(t, gs.bq, gs.pq), notMember(t, gs0.fwriters), notMember(t, gs0.freaders), notMember(t, gs.fwriters), notMember(t, gs.freaders), pendingOk(ags0.p), pendingOk(ags.p), pendingOk(gs0.bq, gs0.pq), pendingOk(gs.bq, gs.pq), pre(gs, ls, ready, callFLITCOMPLETE(ls.t)), readFOsOk(gs0.rfo, gs0.fwriters), readFOsOk(gs.rfo, gs.fwriters), reorder(ags.p, gs.pq, gs.rfo), writersOk(ags0.p, ags0.writers), writersOk(ags.p, ags.writers), writersOk(gs0.bq, gs0.pq, gs0.fwriters), writersOk(gs.bq, gs.pq, gs.fwriters), ¬ SF ∈ gs.bq(t), ¬ SF ∈ gs0.bq(t), pre(ags, als, apc, callPSCCOMPLETE(ls.t)) → ags0 = gstepf(ags, als, apc, callPSCCOMPLETE(ls.t)) ∧ als0 = lstepf(ags, als, apc, callPSCCOMPLETE(ls.t)) ∧ apc0 = pcstepf(ags, als, apc, callPSCCOMPLETE(ls.t)), ∀ t0. t0 ≠ t → FLITLInv(gs, lsf(t0), pcf(t0)) ∧ FLITPSCLInv(ags, alsf(t0), apcf(t0)) ∧ labs(gs, lsf(t0), pcf(t0), ags, alsf(t0), apcf(t0)), ∀ t0. t0 ≠ t → alsf(t0).t = t0, ∀ t0. t0 ≠ t → lsf(t0).t = t0 ⊦ pre(ags, als, apc, callPSCCOMPLETE(ls.t)) ∧ (ags0.mem = gs0.pmem ∧ ags0.ctr = gs0.fctr ∧ reorder(ags0.p, gs0.pq, gs0.rfo) ∧ ags0.writers = gs0.fwriters) ∧ ls0.t = als0.t ∧ apc0 = ready

Rule argument

Additional information

Proof step 2 from proof step-absstep-ready-ready-callFLITCOMPLETE-same (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 3:

  gs.bq(t) = [], ags.ctr = gs.fctr, ags.mem = gs.pmem, gs.rfo(t) = [], alsf(t).t = t, lsf(t).t = t, ags.writers = gs.fwriters, apcf(t) = ready, lsf0(t) = lsf(t), pcf(t) = ready, pcf0(t) = ready, FLITPSCLInv(ags, alsf(t), ready), SFTrailing(gs.bq), ctrok(gs.fctr, gs.fwriters), ctrok(ags0.ctr, ags0.writers), noPendingW(t, gs.bq, gs.pq), notMember(t, gs.freaders), notMember(t, gs.fwriters), pendingOk(gs.bq, gs.pq), pendingOk(ags.p), pendingOk(ags0.p), readFOsOk(gs.rfo, gs.fwriters), reorder(ags.p, gs.pq, gs.rfo), writersOk(gs.bq, gs.pq, gs.fwriters), writersOk(ags.p, gs.fwriters), writersOk(ags0.p, ags0.writers), ¬ FO(t) ∈ gs.pq(l) → ags0 = ags ∧ als0 = alsf(t) ∧ apc0 = ready, ∀ t0. t0 ≠ t → FLITLInv(gs, lsf(t0), pcf(t0)) ∧ FLITPSCLInv(ags, alsf(t0), apcf(t0)) ∧ labs(gs, lsf(t0), pcf(t0), ags, alsf(t0), apcf(t0)), ∀ l. ¬ FO(t) ∈ gs.pq(l), ∀ t0. lsf(t0).t = t0, ∀ t0. alsf(t0).t = t0 ⊦ ¬ FO(als0.t) ∈ gs.pq(l0) ∧ ags0.mem = gs.pmem ∧ ags0.ctr = gs.fctr ∧ reorder(ags0.p, gs.pq, gs.rfo) ∧ ags0.writers = gs.fwriters ∧ t = als0.t ∧ apc0 = ready

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ a ∈ []; (s) ⊦ reorder(p, pq, rfo) → (FO(t) ∈ p(l) ↔ FO(t) ∈ pq(l) ∨ FO(l) ∈ rfo(t)); (s) ⊦ callPSCCOMPLETE(t) = callPSCCOMPLETE(t0) ↔ t = t0; (s) ⊦ callPSCCOMPLETE(t) ≠ invFLITPSCREAD(t0, l); (s) ⊦ callPSCCOMPLETE(t) ≠ invFLITPSCWRITE(t0, l, v); (s) ⊦ pre(gs, ls, ready, a) ↔ (∃ l0, v0. a = invFLITPSCWRITE(ls.t, l0, v0)) ∨ (∃ l0. a = invFLITPSCREAD(ls.t, l0)) ∨ a = callPSCCOMPLETE(ls.t) ∧ (∀ l. ¬ FO(ls.t) ∈ gs.p(l)); (s) ⊦ ls.t = t → pcstepf(gs, ls, ready, callPSCCOMPLETE(t)) = ready; (s) ⊦ ls.t = t → lstepf(gs, ls, ready, callPSCCOMPLETE(t)) = ls; (s) ⊦ gstepf(gs, ls, ready, a) = gs; (s) ⊦ gstepf(gs, ls, ready, a) = gs; (s) ⊦ callFLITCOMPLETE(t) ≠ invFLITREAD(t0, loc); (s) ⊦ callFLITCOMPLETE(t) ≠ invFLITWRITE(t0, loc, v); (s) ⊦ pre(gs, ls, ready, a) ↔ (∃ loc0, val0. a = invFLITWRITE(ls.t, loc0, val0)) ∨ (∃ loc0. a = invFLITREAD(ls.t, loc0)) ∨ a = callFLITCOMPLETE(ls.t) ∧ gs.bq(ls.t) = [] ∧ (∀ l. ¬ FO(ls.t) ∈ gs.pq(l)); (s) ⊦ ls.t = t → lstepf(gs, ls, ready, callFLITCOMPLETE(t)) = ls; (s) ⊦ ls.t = t → pcstepf(gs, ls, ready, callFLITCOMPLETE(t)) = ready; (s)

Proof step 3 from proof step-absstep-ready-ready-callFLITCOMPLETE-same (previous step) (back to tree)

User applied rule all left

And obtained the following new goals

• Proof step 4:

  gs.bq(t) = [], ags.ctr = gs.fctr, ags.mem = gs.pmem, gs.rfo(t) = [], lsf(t).t = t, alsf(t).t = t, ags.writers = gs.fwriters, apcf(t) = ready, lsf0(t) = lsf(t), pcf(t) = ready, pcf0(t) = ready, FLITPSCLInv(ags, alsf(t), ready), SFTrailing(gs.bq), ctrok(ags0.ctr, ags0.writers), ctrok(gs.fctr, gs.fwriters), noPendingW(t, gs.bq, gs.pq), notMember(t, gs.fwriters), notMember(t, gs.freaders), pendingOk(ags0.p), pendingOk(ags.p), pendingOk(gs.bq, gs.pq), readFOsOk(gs.rfo, gs.fwriters), reorder(ags.p, gs.pq, gs.rfo), writersOk(ags0.p, ags0.writers), writersOk(ags.p, gs.fwriters), writersOk(gs.bq, gs.pq, gs.fwriters), ¬ FO(t) ∈ gs.pq(l), ¬ FO(t) ∈ gs.pq(l) → ags0 = ags ∧ als0 = alsf(t) ∧ apc0 = ready, ∀ t0. alsf(t0).t = t0, ∀ t0. lsf(t0).t = t0, ∀ l. ¬ FO(t) ∈ gs.pq(l), ∀ t0. t0 ≠ t → FLITLInv(gs, lsf(t0), pcf(t0)) ∧ FLITPSCLInv(ags, alsf(t0), apcf(t0)) ∧ labs(gs, lsf(t0), pcf(t0), ags, alsf(t0), apcf(t0)) ⊦ ¬ FO(als0.t) ∈ gs.pq(l0) ∧ ags0.mem = gs.pmem ∧ ags0.ctr = gs.fctr ∧ reorder(ags0.p, gs.pq, gs.rfo) ∧ ags0.writers = gs.fwriters ∧ t = als0.t ∧ apc0 = ready

Rule argument

Additional information

Used terms: l

Proof step 4 from proof step-absstep-ready-ready-callFLITCOMPLETE-same (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 5:

  gs.bq(t) = [], ags.ctr = gs.fctr, ags.mem = gs.pmem, gs.rfo(t) = [], lsf(t).t = t, alsf(t).t = t, ags.writers = gs.fwriters, apcf(t) = ready, lsf0(t) = lsf(t), pcf(t) = ready, pcf0(t) = ready, FLITPSCLInv(ags, alsf(t), ready), SFTrailing(gs.bq), ctrok(gs.fctr, gs.fwriters), noPendingW(t, gs.bq, gs.pq), notMember(t, gs.fwriters), notMember(t, gs.freaders), pendingOk(ags.p), pendingOk(gs.bq, gs.pq), readFOsOk(gs.rfo, gs.fwriters), reorder(ags.p, gs.pq, gs.rfo), writersOk(ags.p, gs.fwriters), writersOk(gs.bq, gs.pq, gs.fwriters), FO(t) ∈ gs.pq(l0), ¬ FO(t) ∈ gs.pq(l), ∀ t0. alsf(t0).t = t0, ∀ t0. lsf(t0).t = t0, ∀ l. ¬ FO(t) ∈ gs.pq(l), ∀ t0. t0 ≠ t → FLITLInv(gs, lsf(t0), pcf(t0)) ∧ FLITPSCLInv(ags, alsf(t0), apcf(t0)) ∧ labs(gs, lsf(t0), pcf(t0), ags, alsf(t0), apcf(t0)) ⊦

Rule argument

Additional information

Proof step 5 from proof step-absstep-ready-ready-callFLITCOMPLETE-same (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: l0