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Proof step 38 from proof inv-commit (previous step)

zh[rp] = mkznode(r, zbrar, boolvar, true, m), adr3 = adr, err1 = ESUCCESS, istore = istore3[n, indexblock([], [], 0)], pstate = index(n), remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, syn0, elems nx ∩ ginval4 = ∅, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, btree-inv(rp, adr, istore3[n, indexblock([], [], 0)], istore1, zh, ri, fi), btree-inv(rp, adr, istore3, istore1, zh, ri, fi), inv(istore3[n, indexblock([], [], 0)]), inv(istore1), inv(istore3), inv(gstore1), inv(gstore2 \ ginval4), rp ∈ zh, istore1 ⊑ istore3[n, indexblock([], [], 0)], istore1 ⊑ istore3 ⊦ ∀ adr, err1, zh, istore, pstate, syn0. istore3[n, indexblock([], [], 0)] ⊑ istore ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn0) ∧ inv(istore) ∧ istore1 ⊑ istore ∧ (err1 ≠ ESUCCESS → btree-inv(rp, adr3, istore, istore1, zh, ri, fi)) ∧ ( err1 = ESUCCESS → btree-inv(rp, adr, istore, istore, zh, ri, ri) ∧ btree-inv (rp, adr3, istore[adr.lnum, istore[adr.lnum].ref-size:= (istore[adr.lnum].ref-size - adr.size)], istore1, zh[rp, zh[rp].dirty:= true], ri, fi) ∧ ¬ zh[rp].dirty) → ⟪syn := false; adr0 := adr3; if err1 = ESUCCESS then {syn := true; apersistence_sync#(adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; pstate, syn0; err1)}; if err1 = ESUCCESS then apersistence_commit#(adr, maxino1, syn0; ginval1, adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate; err1); if err1 = ESUCCESS then adr3 := adr else if syn then {zh[rp].dirty := true; let maxino = 0 in {apersistence_get_iblock_refsize# (adr.lnum, adr0, istore, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate, syn0; ; maxino); apersistence_set_iblock_refsize# (adr.lnum, maxino - adr.size, adr0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate, syn0; istore)}}⟫ ( (∃ ri, fi. btree-inv(rp, adr0, istore, istore1, zh, ri, fi)) ∧ inv(gstore2 \ ginval4) ∧ inv(gstore1) ∧ elems nx ∩ ginval4 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4 ∧ remove-refsize0(gstore1) = gstore1 ∧ inv(istore) ∧ inv(istore1) ∧ istore1 ⊑ istore ∧ remove-refsize0(istore1) = istore1 ∧ (pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore2) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn0)), dups(nx), n ∈ istore3

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 39:
zh[rp] = mkznode(r, zbrar, boolvar, true, m), remove-refsize0(gstore1) = gstore1, remove-refsize0(istore1) = istore1, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, elems nx ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, btree-inv(rp, adr, istore3, istore1, zh, ri, fi), btree-inv(rp, adr, istore3[n, indexblock([], [], 0)], istore1, zh, ri, fi), inv(istore0), inv(gstore2 \ ginval4), inv(gstore1), inv(istore3), inv(istore1), inv(istore3[n, indexblock([], [], 0)]), rp ∈ zh, istore3[n, indexblock([], [], 0)] ⊑ istore0, istore1 ⊑ istore3, istore1 ⊑ istore3[n, indexblock([], [], 0)], istore1 ⊑ istore0, ¬ dups(nx), ¬ n ∈ istore3, pstate0.journal? → nx ≠ [] ∧ pstate0.lnum = nx.last ∧ pstate0.lnum ∈ gstore2, pstate0.index? → pstate0.lnum ∈ istore0, pstate0 = unbuffered → syn1, err ≠ ESUCCESS → btree-inv(rp, adr, istore0, istore1, zh0, ri, fi), err = ESUCCESS → btree-inv(rp, adr1, istore0, istore0, zh0, ri, ri) ∧ btree-inv (rp, adr, istore0[adr1.lnum, istore0[adr1.lnum].ref-size:= (istore0[adr1.lnum].ref-size - adr1.size)], istore1, zh0[rp, zh0[rp].dirty:= true], ri, fi) ∧ ¬ zh0[rp].dirty ⊦ ⟪syn := false; adr0 := adr; if err = ESUCCESS then {syn := true; apersistence_sync#(adr0, istore0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval; pstate0, syn1; err)}; if err = ESUCCESS then apersistence_commit#(adr1, maxino1, syn1; ginval1, adr0, istore0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate0; err); if err = ESUCCESS then adr := adr1 else if syn then {zh0[rp].dirty := true; let maxino = 0 in {apersistence_get_iblock_refsize# (adr1.lnum, adr0, istore0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate0, syn1; ; maxino); apersistence_set_iblock_refsize# (adr1.lnum, maxino - adr1.size, adr0, istore1, ginval4, gstore2, gstore1, nx, maxino0, ginval, pstate0, syn1; istore0)}}⟫ ( (∃ ri, fi. btree-inv(rp, adr0, istore0, istore1, zh0, ri, fi)) ∧ inv(gstore2 \ ginval4) ∧ inv(gstore1) ∧ elems nx ∩ ginval4 = ∅ ∧ ¬ dups(nx) ∧ dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4 ∧ remove-refsize0(gstore1) = gstore1 ∧ inv(istore0) ∧ inv(istore1) ∧ istore1 ⊑ istore0 ∧ remove-refsize0(istore1) = istore1 ∧ (pstate0.journal? → nx ≠ [] ∧ pstate0.lnum = nx.last ∧ pstate0.lnum ∈ gstore2) ∧ (pstate0.index? → pstate0.lnum ∈ istore0) ∧ (pstate0 = unbuffered → syn1))

Rule argument

Additional information

Used simplifier rules: prefix-trans: ⊦ istore ⊑ istore0 ∧ istore0 ⊑ istore1 → istore ⊑ istore1; (forward) from specification ablock-store-inv[index-store]