Proof step 1 from proof rely-R2-R4 (conclusion) (back to tree)

System applied rule normalize

And obtained the following new goals

• Proof step 2:

  gs.rfo(ls.t) = gs.bq(ls.t), pcstepf(gs, ls, R2, a) = R4, ls.t ≠ t0, SFTrailing(gs.bq), ctrok(gs.fctr, gs.fwriters), noPendingW(ls.t, gs.bq, gs.pq), notMember(ls.t, gs.fwriters), oneMember(ls.t, ls.loc, gs.freaders), pendingOk(gs.bq, gs.pq), pre(gs, ls, R2, a), readFOsOk(gs.rfo, gs.fwriters), writersOk(gs.bq, gs.pq, gs.fwriters), ¬ SF ∈ gs.bq(ls.t) ⊦ relyws(t0, gs.freaders, gstepf(gs, ls, R2, a).freaders) ∧ relyws(t0, gs.fwriters, gstepf(gs, ls, R2, a).fwriters) ∧ rely(t0, gs.pq, gs.bq, gstepf(gs, ls, R2, a).pq, gstepf(gs, ls, R2, a).bq) ∧ gs.bq(t0) ⊒w gstepf(gs, ls, R2, a).bq(t0) ∧ (gs.rfo(t0) = [] → gstepf(gs, ls, R2, a).rfo(t0) = []) ∧ (gs.rfo(t0) = gs.bq(t0) → gstepf(gs, ls, R2, a).rfo(t0) = gstepf(gs, ls, R2, a).bq(t0)) ∧ ( gs.rfo(t0) + SF ' = gs.bq(t0) → gstepf(gs, ls, R2, a).rfo(t0) + SF ' = gstepf(gs, ls, R2, a).bq(t0) ∨ gstepf(gs, ls, R2, a).rfo(t0) = gstepf(gs, ls, R2, a).bq(t0))

Rule argument

Additional information

Proof step 2 from proof rely-R2-R4 (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ (gs.freaders:= fwriters0).bq = gs.bq; (s) ⊦ gstepf(gs, ls, R2, a) = (gs.fctr(ls.loc) ≠ 0 ⊃ gs ;gs.freaders:= gs.freaders(ls.loc := gs.freaders(ls.loc) -- ls.t) ); (s) ⊦ (gs.freaders:= fwriters0).rfo = gs.rfo; (s) ⊦ bel ⊒w bel; (s) ⊦ rely(t, pq, bq, pq, bq); (s) ⊦ (gs.freaders:= fwriters0).pq = gs.pq; (s) ⊦ relyws(t, tsf, tsf); (s) ⊦ (gs.freaders:= fwriters0).fwriters = gs.fwriters; (s) ⊦ t ≠ t0 → relyws(t, tsf, tsf(l := tsf(l) -- t0)); (ss) ⊦ (gs.freaders:= fwriters0).freaders = fwriters0; (s) ⊦ pre(gs, ls, R2, a) ↔ a = ctrRead(ls.t, ls.loc, gs.fctr(ls.loc)); (s) ⊦ R3 ≠ R4; (s) ⊦ pcstepf(gs, ls, R2, a) = (gs.fctr(ls.loc) ≠ 0 ⊃ R3;R4); (s)