Proof step 1 from proof step-absstep-ready-R1-invFLITREAD-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, R1 = pcstepf(gs, ls, ready, invFLITREAD(ls.t, loc0)), alsf(t) = als, apc = ready, apcf(t) = apc, gs0 = gstepf(gs, ls, ready, invFLITREAD(ls.t, loc0)), ls0 = lstepf(gs, ls, ready, invFLITREAD(ls.t, loc0)), lsf(t) = ls, lsf0(t) = ls0, pcf(t) = ready, pcf0(t) = R1, 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, invFLITREAD(ls.t, loc0)), 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, invFLITPSCREAD(ls.t, loc0)) → ags0 = gstepf(ags, als, apc, invFLITPSCREAD(ls.t, loc0)) ∧ als0 = lstepf(ags, als, apc, invFLITPSCREAD(ls.t, loc0)) ∧ apc0 = pcstepf(ags, als, apc, invFLITPSCREAD(ls.t, loc0)), ∀ 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, invFLITPSCREAD(ls.t, loc0)) ∧ (ags0.mem = gs0.pmem ∧ ags0.ctr = gs0.fctr ∧ reorder(ags0.p, gs0.pq, gs0.rfo) ∧ ags0.writers = gs0.fwriters) ∧ ls0.t = als0.t ∧ apc0 = R1 ∧ ls0.loc = als0.l

Rule argument

Additional information

Proof step 2 from proof step-absstep-ready-R1-invFLITREAD-same (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 3:

  ags.ctr = gs.fctr, ags.mem = gs.pmem, gs.rfo(t) = gs.bq(t), alsf(t).t = t, lsf(t).t = t, ags.writers = gs.fwriters, apcf(t) = ready, lsf0(t) = lsf(t).loc:= loc0, pcf(t) = ready, pcf0(t) = R1, FLITPSCLInv(ags, alsf(t), ready), SFTrailing(gs.bq), ctrok(gs.fctr, gs.fwriters), noPendingW(t, gs.bq, gs.pq), notMember(t, gs.freaders), notMember(t, gs.fwriters), pendingOk(gs.bq, gs.pq), pendingOk(ags.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), ¬ SF ∈ gs.bq(t), ∀ t0. lsf(t0).t = t0, ∀ t0. alsf(t0).t = t0, ∀ 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)) ⊦ lsf0(t).t = t ∧ lsf0(t).loc = loc0

Rule argument

Additional information

Used simplifier rules: ⊦ (ls.l:= l).l = l; (s) ⊦ (ls.l:= l).t = ls.t; (s) ⊦ invFLITPSCREAD(t, l) = invFLITPSCREAD(t0, l0) ↔ t = t0 ∧ l = l0; (ws) ⊦ invFLITPSCREAD(t, l) ≠ invFLITPSCWRITE(t0, l0, 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, invFLITPSCREAD(t, l0)) = R1; (s) ⊦ ls.t = t → lstepf(gs, ls, ready, invFLITPSCREAD(t, l0)) = ls.l:= l0; (s) ⊦ gstepf(gs, ls, ready, a) = gs; (s) ⊦ gstepf(gs, ls, ready, a) = gs; (s) ⊦ invFLITREAD(t, loc) = invFLITREAD(t0, loc0) ↔ t = t0 ∧ loc = loc0; (ws) ⊦ callFLITCOMPLETE(t) ≠ invFLITREAD(t0, loc); (s) ⊦ invFLITREAD(t, loc) ≠ invFLITWRITE(t0, loc0, 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 → pcstepf(gs, ls, ready, invFLITREAD(t, loc0)) = R1; (s) ⊦ ls.t = t → lstepf(gs, ls, ready, invFLITREAD(t, loc0)) = ls.loc:= loc0; (s)

Proof step 3 from proof step-absstep-ready-R1-invFLITREAD-same (previous step) (back to tree)

Heuristic elimination applied rule apply elim lemma

And obtained the following new goals

• Proof step 4:

  gs.rfo(t) = gs.bq(t), lsf(t).t = t, alsf(t).t = t, ags = mkFLITPSCgs(mem, p, ctr, writers, writers0), apcf(t) = ready, ctr = gs.fctr, lsf0(t) = lsf(t).loc:= loc0, mem = gs.pmem, pcf(t) = ready, pcf0(t) = R1, writers = gs.fwriters, 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(p), pendingOk(gs.bq, gs.pq), readFOsOk(gs.rfo, gs.fwriters), reorder(p, gs.pq, gs.rfo), writersOk(p, gs.fwriters), writersOk(gs.bq, gs.pq, gs.fwriters), ¬ SF ∈ gs.bq(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. alsf(t0).t = t0, ∀ t0. lsf(t0).t = t0 ⊦ lsf0(t).t = t ∧ lsf0(t).loc = loc0

Rule argument

Additional information

Used simplifier rules: ⊦ (((mem = gs.mem ∧ p = gs.p) ∧ ctr = gs.ctr) ∧ writers = gs.writers) ∧ readers = gs.readers ↔ gs = mkFLITPSCgs(mem, p, ctr, writers, readers); (elim) Used terms: ags, mem, ctr, writers, writers0, p

Proof step 4 from proof step-absstep-ready-R1-invFLITREAD-same (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 5:

  gs.rfo(t) = gs.bq(t), alsf(t).t = t, lsf(t).t = t, apcf(t) = ready, lsf0(t) = lsf(t).loc:= loc0, pcf(t) = ready, pcf0(t) = R1, FLITPSCLInv(mkFLITPSCgs(gs.pmem, p, gs.fctr, gs.fwriters, writers0), alsf(t), ready), SFTrailing(gs.bq), ctrok(gs.fctr, gs.fwriters), noPendingW(t, gs.bq, gs.pq), notMember(t, gs.freaders), notMember(t, gs.fwriters), pendingOk(gs.bq, gs.pq), pendingOk(p), readFOsOk(gs.rfo, gs.fwriters), reorder(p, gs.pq, gs.rfo), writersOk(gs.bq, gs.pq, gs.fwriters), writersOk(p, gs.fwriters), ¬ SF ∈ gs.bq(t), ∀ t0. lsf(t0).t = t0, ∀ t0. alsf(t0).t = t0, ∀ t0. t0 ≠ t → FLITLInv(gs, lsf(t0), pcf(t0)) ∧ FLITPSCLInv(mkFLITPSCgs(gs.pmem, p, gs.fctr, gs.fwriters, writers0), alsf(t0), apcf(t0)) ∧ labs(gs, lsf(t0), pcf(t0), mkFLITPSCgs(gs.pmem, p, gs.fctr, gs.fwriters, writers0), alsf(t0), apcf(t0)) ⊦ lsf0(t).t = t ∧ lsf0(t).loc = loc0

Rule argument

Additional information

Proof step 5 from proof step-absstep-ready-R1-invFLITREAD-same (previous step) (back to tree)

Heuristic elimination applied rule apply elim lemma

And obtained the following new goals

• Proof step 6:

  gs.rfo(t) = gs.bq(t), lsf(t).t = t, alsf(t) = mkFLITPSCls(t1, l, v), apcf(t) = ready, lsf0(t) = lsf(t).loc:= loc0, pcf(t) = ready, pcf0(t) = R1, t1 = t, FLITPSCLInv(mkFLITPSCgs(gs.pmem, p, gs.fctr, gs.fwriters, writers0), 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(p), pendingOk(gs.bq, gs.pq), readFOsOk(gs.rfo, gs.fwriters), reorder(p, gs.pq, gs.rfo), writersOk(p, gs.fwriters), writersOk(gs.bq, gs.pq, gs.fwriters), ¬ SF ∈ gs.bq(t), ∀ t0. t0 ≠ t → FLITLInv(gs, lsf(t0), pcf(t0)) ∧ FLITPSCLInv(mkFLITPSCgs(gs.pmem, p, gs.fctr, gs.fwriters, writers0), alsf(t0), apcf(t0)) ∧ labs(gs, lsf(t0), pcf(t0), mkFLITPSCgs(gs.pmem, p, gs.fctr, gs.fwriters, writers0), alsf(t0), apcf(t0)), ∀ t0. alsf(t0).t = t0, ∀ t0. lsf(t0).t = t0 ⊦ lsf0(t).t = t ∧ lsf0(t).loc = loc0

Rule argument

Additional information

Used simplifier rules: ⊦ (t = ls.t ∧ l = ls.l) ∧ v = ls.v ↔ ls = mkFLITPSCls(t, l, v); (elim) Used terms: alsf(t), t1, l, v

Proof step 6 from proof step-absstep-ready-R1-invFLITREAD-same (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 7:

  gs.rfo(t) = gs.bq(t), lsf(t).t = t, alsf(t) = mkFLITPSCls(t, l, v), apcf(t) = ready, lsf0(t) = lsf(t).loc:= loc0, pcf(t) = ready, pcf0(t) = R1, FLITPSCLInv(mkFLITPSCgs(gs.pmem, p, gs.fctr, gs.fwriters, writers0), mkFLITPSCls(t, l, v), ready), SFTrailing(gs.bq), ctrok(gs.fctr, gs.fwriters), noPendingW(t, gs.bq, gs.pq), notMember(t, gs.freaders), notMember(t, gs.fwriters), pendingOk(gs.bq, gs.pq), pendingOk(p), readFOsOk(gs.rfo, gs.fwriters), reorder(p, gs.pq, gs.rfo), writersOk(gs.bq, gs.pq, gs.fwriters), writersOk(p, gs.fwriters), ¬ SF ∈ gs.bq(t), ∀ t0. lsf(t0).t = t0, ∀ t0. alsf(t0).t = t0, ∀ t0. t0 ≠ t → FLITLInv(gs, lsf(t0), pcf(t0)) ∧ FLITPSCLInv(mkFLITPSCgs(gs.pmem, p, gs.fctr, gs.fwriters, writers0), alsf(t0), apcf(t0)) ∧ labs(gs, lsf(t0), pcf(t0), mkFLITPSCgs(gs.pmem, p, gs.fctr, gs.fwriters, writers0), alsf(t0), apcf(t0)) ⊦ lsf0(t).t = t ∧ lsf0(t).loc = loc0

Rule argument

Additional information

Proof step 7 from proof step-absstep-ready-R1-invFLITREAD-same (previous step) (back to tree)

User applied rule subst equation

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ (ls.loc:= loc).t = ls.t; (s) ⊦ (ls.loc:= loc).loc = loc; (s)