Proof step 1 from proof step-absstep-W2-W3-ctrInc-same (conclusion) (back to tree)

System applied rule normalize

And obtained the following new goals

• Proof step 2:

  gs0.bq(t) = [], ags.ctr = gs.fctr, ls.loc = als.l, ags.mem = gs.pmem, gs0.rfo(t) = [], ls.t = als.t, lsf(t).t = t, alsf(t).t = t, ls.val = als.v, ags.writers = gs.fwriters, W3 = pcstepf(gs, ls, W2, ctrInc(ls.t, loc)), alsf(t) = als, apc = (SF ∈ gs.bq(ls.t) ⊃ W1;W2), apcf(t) = apc, gs0 = gstepf(gs, ls, W2, ctrInc(ls.t, loc)), ls0 = lstepf(gs, ls, W2, ctrInc(ls.t, loc)), lsf(t) = ls, lsf0(t) = ls0, pcf(t) = W2, pcf0(t) = W3, 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), noPending(t, gs0.bq, gs0.pq), noPendingW(t, gs.bq, gs.pq), notMember(t, gs0.freaders), notMember(t, gs.freaders), notMember(t, gs.fwriters), oneMember(t, ls0.loc, gs0.fwriters), pendingOk(ags0.p), pendingOk(ags.p), pendingOk(gs0.bq, gs0.pq), pendingOk(gs.bq, gs.pq), pre(gs, ls, W2, ctrInc(ls.t, loc)), 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 ∈ gs0.bq(t), pre(ags, als, apc, ctrIncPSC(ls.t, loc)) → ags0 = gstepf(ags, als, apc, ctrIncPSC(ls.t, loc)) ∧ als0 = lstepf(ags, als, apc, ctrIncPSC(ls.t, loc)) ∧ apc0 = pcstepf(ags, als, apc, ctrIncPSC(ls.t, loc)), ∀ 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, gs.rfo(t) = gs.bq(t) ∨ gs.rfo(t) + SF ' = gs.bq(t) ⊦ pre(ags, als, apc, ctrIncPSC(ls.t, loc)) ∧ (ags0.mem = gs0.pmem ∧ ags0.ctr = gs0.fctr ∧ reorder(ags0.p, gs0.pq, gs0.rfo) ∧ ags0.writers = gs0.fwriters) ∧ ls0.t = als0.t ∧ apc0 = W3 ∧ ls0.loc = als0.l ∧ ls0.val = als0.v

Rule argument

Additional information

Proof step 2 from proof step-absstep-W2-W3-ctrInc-same (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ (gs.writers:= writers).writers = writers; (s) ⊦ (gs.ctr:= ctr).p = gs.p; (s) ⊦ (gs.writers:= writers).p = gs.p; (s) ⊦ (gs.ctr:= ctr).ctr = ctr; (s) ⊦ (gs.writers:= writers).ctr = gs.ctr; (s) ⊦ (gs.ctr:= ctr).mem = gs.mem; (s) ⊦ (gs.writers:= writers).mem = gs.mem; (s) ⊦ ctrIncPSC(t, l) = ctrIncPSC(t0, l0) ↔ t = t0 ∧ l = l0; (ws) ⊦ pre(gs, ls, W2, a) ↔ a = ctrIncPSC(ls.t, ls.l); (s) ⊦ ¬ a ∈ []; (s) ⊦ pcstepf(gs, ls, W2, a) = W3; (s) ⊦ lstepf(gs, ls, W2, a) = ls; (s) ⊦ gstepf(gs, ls, W2, a) = (gs.ctr:= gs.ctr(ls.l := gs.ctr(ls.l) + 1)) .writers:= gs.writers(ls.l := gs.writers(ls.l) ++ ls.t); (s) ⊦ (gs.fwriters:= fwriters).fwriters = fwriters; (s) ⊦ gstepf(gs, ls, W2, a) = (gs.fctr:= gs.fctr(ls.loc := gs.fctr(ls.loc) + 1)) .fwriters:= gs.fwriters(ls.loc := gs.fwriters(ls.loc) ++ ls.t); (s) ⊦ (gs.fctr:= fctr).rfo = gs.rfo; (s) ⊦ (gs.fwriters:= fwriters).rfo = gs.rfo; (s) ⊦ (gs.fctr:= fctr).pq = gs.pq; (s) ⊦ (gs.fwriters:= fwriters).pq = gs.pq; (s) ⊦ (gs.fctr:= fctr).fctr = fctr; (s) ⊦ (gs.fwriters:= fwriters).fctr = gs.fctr; (s) ⊦ (gs.fctr:= fctr).pmem = gs.pmem; (s) ⊦ (gs.fwriters:= fwriters).pmem = gs.pmem; (s) ⊦ (gs.fctr:= fctr).bq = gs.bq; (s) ⊦ (gs.fwriters:= fwriters).bq = gs.bq; (s) ⊦ (gs.fctr:= fctr).freaders = gs.freaders; (s) ⊦ (gs.fwriters:= fwriters).freaders = gs.freaders; (s) ⊦ ctrInc(t, loc) = ctrInc(t0, loc0) ↔ t = t0 ∧ loc = loc0; (ws) ⊦ pre(gs, ls, W2, a) ↔ (gs.bq(ls.t) = [] ∧ (∀ l. ¬ FO(ls.t) ∈ gs.pq(l))) ∧ a = ctrInc(ls.t, ls.loc); (s) ⊦ pcstepf(gs, ls, W2, a) = W3; (s) ⊦ lstepf(gs, ls, W2, a) = ls; (s)