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Proof step 227 from proof inv-commit (previous step)

syn ↔ false, istore2[m0] = indexblock(indx, lax, m3), zh[rp] = mkznode(r, zbrar, boolvar, true, m), zh0[rp] = mkznode(r0, zbrar0, boolvar0, false, m4), ginval0 = ginval4, gstore = gstore1, gstore0 = gstore2, istore = istore2, istore0 = istore1, maxino = maxino1, maxino0 = m0, n = istore2[m0].ref-size - m2, pstate = pstate1, remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval4 = ∅, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, btree-inv(rp, adr, istore3[n0, indexblock([], [], 0)], istore1, zh, ri, fi), btree-inv(rp, adr, istore3, istore1, zh, ri, fi), btree-inv(rp, @(m0, m1, m2), istore2, istore2, zh0, ri, ri), btree-inv(rp, adr, istore2[m0, indexblock(indx, lax, m3 - m2)], istore1, zh0[rp, mkznode(r0, zbrar0, boolvar0, true, m4)], ri, fi), inv(istore[maxino0, istore[maxino0].ref-size:= n]), inv(indexblock(indx, lax, m3)), inv(istore3[n0, indexblock([], [], 0)]), inv(istore1), inv(istore3), inv(gstore1), inv(gstore2 \ ginval4), inv(istore2), maxino0 ∈ istore, rp ∈ zh, m0 ∈ istore2, istore2[m0].ref-size ≥ m2, istore1 ⊑ istore[maxino0, istore[maxino0].ref-size:= n], istore1 ⊑ istore2, istore1 ⊑ istore3[n0, indexblock([], [], 0)], istore1 ⊑ istore3, istore3[n0, indexblock([], [], 0)] ⊑ istore2, ⌊err⌋ , pstate1.index? → pstate1.lnum ∈ istore[maxino0, istore[maxino0].ref-size:= n], pstate1.index? → pstate1.lnum ∈ istore2, pstate1.journal? → nx ≠ [] ∧ pstate1.lnum = nx.last ∧ pstate1.lnum ∈ gstore2 ⊦ pstate1 = unbuffered, pstate1 = readonly, dups(nx), n0 ∈ istore3, ∃ ri0, fi0. btree-inv(rp, adr, istore[maxino0, istore[maxino0].ref-size:= n], istore1, zh0[rp, mkznode(r0, zbrar0, boolvar0, true, m4)], ri0, fi0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 228:
istore2[m0] = indexblock(indx, lax, m3), zh[rp] = mkznode(r, zbrar, boolvar, true, m), zh0[rp] = mkznode(r0, zbrar0, boolvar0, false, m4), remove-refsize0(istore1) = istore1, remove-refsize0(gstore1) = gstore1, elems nx ∩ ginval4 = ∅, dom remove-refsize0(gstore2) ∩ ginval4 = ∅, dom gstore1 ∪ elems nx = dom gstore2 ∪ ginval4, btree-inv(rp, adr, istore3[n0, indexblock([], [], 0)], istore1, zh, ri, fi), btree-inv(rp, adr, istore3, istore1, zh, ri, fi), btree-inv(rp, @(m0, m1, m2), istore2, istore2, zh0, ri, ri), btree-inv(rp, adr, istore2[m0, indexblock(indx, lax, m3 - m2)], istore1, zh0[rp, mkznode(r0, zbrar0, boolvar0, true, m4)], ri, fi), inv(indexblock(indx, lax, m3)), inv(istore3[n0, indexblock([], [], 0)]), inv(istore1), inv(istore3), inv(gstore1), inv(gstore2 \ ginval4), inv(istore2), inv(istore2[m0, indexblock(indx, lax, m3 - m2)]), rp ∈ zh, m0 ∈ istore2, m2 ≤ m3, istore1 ⊑ istore2, istore1 ⊑ istore2[m0, indexblock(indx, lax, m3 - m2)], istore1 ⊑ istore3[n0, indexblock([], [], 0)], istore1 ⊑ istore3, istore3[n0, indexblock([], [], 0)] ⊑ istore2, ⌊err⌋ , pstate1.index? → pstate1.lnum ∈ istore2, pstate1.journal? → nx ≠ [] ∧ pstate1.lnum = nx.last ∧ pstate1.lnum ∈ gstore2, pstate1.index? → pstate1.lnum ∈ istore2[m0, indexblock(indx, lax, m3 - m2)] ⊦ pstate1 = unbuffered, pstate1 = readonly, dups(nx), n0 ∈ istore3, ∃ ri0, fi0. btree-inv(rp, adr, istore2[m0, indexblock(indx, lax, m3 - m2)], istore1, zh0[rp, mkznode(r0, zbrar0, boolvar0, true, m4)], ri0, fi0)

Rule argument

Additional information

Used simplifier rules: ⊦ indexblock(indx, lax, m).ref-size:= m0 = indexblock(indx, lax, m0); (s)% ⊦ indexblock(indx, lax, m).ref-size = m; (s)%prefix-trans: ⊦ istore ⊑ istore0 ∧ istore0 ⊑ istore1 → istore ⊑ istore1; (forward) from specification ablock-store-inv[index-store]% ⊦ n ≥ m ↔ m ≤ n; (s)