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Proof step 285 from proof inv-commit (previous step)

istore0[m0] = indexblock(indx, lax, m3), zh[rp] = mkznode(r, zbrar, boolvar, true, m), zh0[rp] = mkznode(r0, zbrar0, boolvar0, false, m4), remove-refsize0(istore2) = istore2, remove-refsize0(gstore3) = gstore3, elems nx ∩ ginval1 = ∅, dom remove-refsize0(gstore4) ∩ ginval1 = ∅, dom gstore3 ∪ elems nx = dom gstore4 ∪ ginval1, pstate1 ≠ readonly, pstate1 ≠ unbuffered, btree-inv(rp, adr, istore3[n, indexblock([], [], 0)], istore2, zh, ri, fi), btree-inv(rp, adr, istore3, istore2, zh, ri, fi), btree-inv(rp, @(m0, m1, m2), istore0, istore0, zh0, ri, ri), btree-inv(rp, adr, istore0[m0, indexblock(indx, lax, m3 - m2)], istore2, zh0[rp, mkznode(r0, zbrar0, boolvar0, true, m4)], ri, fi), inv(istore3[n, indexblock([], [], 0)]), inv(istore3), inv(istore0), inv(istore2), inv(gstore3), inv(gstore4 \ ginval1), inv(indexblock(indx, lax, m3)), rp ∈ zh, m0 ∈ istore0, istore2 ⊑ istore3[n, indexblock([], [], 0)], istore2 ⊑ istore3, istore3[n, indexblock([], [], 0)] ⊑ istore0, istore2 ⊑ istore0, ⌊err⌋ , ¬ dups(nx), ¬ n ∈ istore3, pstate1.index? → pstate1.lnum ∈ istore0, pstate1.journal? → nx ≠ [] ∧ pstate1.lnum = nx.last ∧ pstate1.lnum ∈ gstore4 ⊦ ⟪apersistence_set_iblock_refsize# (m0, istore0[m0].ref-size - m2, adr, istore2, ginval1, gstore4, gstore3, nx, maxino2, ginval, readonly, true; istore0)⟫ ( (∃ ri0, fi0. btree-inv(rp, adr, istore0, istore2, zh0[rp, mkznode(r0, zbrar0, boolvar0, true, m4)], ri0, fi0)) ∧ inv(istore0) ∧ istore2 ⊑ istore0)

User applied rule insert program lemma

And obtained the following new goals

Proof step 286:
inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), inv-state(pstate, nx, gstore, istore, syn), maxino ∈ istore ⊦ ⟪apersistence_set_iblock_refsize#(maxino, n, adr, istore0, ginval, gstore, gstore0, nx, maxino0, ginval0, pstate, syn; istore)⟫ (inv-index(istore, istore0) ∧ inv-state(pstate, nx, gstore, istore, syn))
Proof step 287:
syn0 ↔ true, zh0[rp] = mkznode(r0, zbrar0, boolvar0, false, m4), zh[rp] = mkznode(r, zbrar, boolvar, true, m), istore0[m0] = indexblock(indx, lax, m3), adr0 = adr, ginval2 = ginval1, ginval3 = ginval, gstore1 = gstore4, gstore2 = gstore3, istore1 = istore2, maxino1 = m0, maxino3 = maxino2, n0 = istore0[m0].ref-size - m2, nx0 = nx, pstate0 = readonly, remove-refsize0(gstore3) = gstore3, remove-refsize0(istore2) = istore2, dom remove-refsize0(gstore4) ∩ ginval1 = ∅, elems nx ∩ ginval1 = ∅, dom gstore3 ∪ elems nx = dom gstore4 ∪ ginval1, btree-inv(rp, adr, istore0[m0, indexblock(indx, lax, m3 - m2)], istore2, zh0[rp, mkznode(r0, zbrar0, boolvar0, true, m4)], ri, fi), btree-inv(rp, @(m0, m1, m2), istore0, istore0, zh0, ri, ri), btree-inv(rp, adr, istore3, istore2, zh, ri, fi), btree-inv(rp, adr, istore3[n, indexblock([], [], 0)], istore2, zh, ri, fi), inv(indexblock(indx, lax, m3)), inv(gstore4 \ ginval1), inv(gstore3), inv(istore2), inv(istore0), inv(istore3), inv(istore3[n, indexblock([], [], 0)]), inv-index(istore0, istore2), inv-journal(nx, gstore4, gstore3, ginval1), inv-state(readonly, nx, gstore4, istore0, true), rp ∈ zh, m0 ∈ istore0, istore2 ⊑ istore0, istore3[n, indexblock([], [], 0)] ⊑ istore0, istore2 ⊑ istore3, istore2 ⊑ istore3[n, indexblock([], [], 0)], ⌊err⌋ , pstate1.journal? → nx ≠ [] ∧ pstate1.lnum = nx.last ∧ pstate1.lnum ∈ gstore4, pstate1.index? → pstate1.lnum ∈ istore0 ⊦ [apersistence_set_iblock_refsize# (m0, istore0[m0].ref-size - m2, adr, istore2, ginval1, gstore4, gstore3, nx, maxino2, ginval, readonly, true; istore0)] ( inv-index(istore0, istore1) ∧ inv-state(pstate0, nx0, gstore1, istore0, syn0) → (∃ ri0, fi0. btree-inv(rp, adr, istore0, istore2, zh0[rp, mkznode(r0, zbrar0, boolvar0, true, m4)], ri0, fi0)) ∧ inv(istore0) ∧ istore2 ⊑ istore0), pstate1 = readonly, pstate1 = unbuffered, dups(nx), n ∈ istore3

Rule argument

spec: apersistence-asm name: inv-set-iblock-refsize seq: inv-journal(nx, gstore, gstore0, ginval), inv-index(istore, istore0), inv-state(pstate, nx, gstore, istore, syn), maxino ∈ istore ⊦ ⟪apersistence_set_iblock_refsize# (maxino, n, adr, istore0, ginval, gstore, gstore0, nx, maxino0, ginval0, pstate, syn ; istore)⟫ ( inv-index(istore, istore0) ∧ inv-state(pstate, nx, gstore, istore, syn)) subst: [syn, pstate, ginval0, maxino0, nx, gstore0, gstore, ginval, istore0, adr, n, maxino, istore] → [true, readonly, ginval, maxino2, nx, gstore3, gstore4, ginval1, istore2, adr, istore0[m0].ref-size - m2, m0, istore0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ inv-journal(nx, gstore, gstore0, ginval) ↔ inv(gstore \ ginval) ∧ inv(gstore0) ∧ elems nx ∩ ginval = ∅ ∧ ¬ dups(nx) ∧ dom gstore0 ∪ elems nx = dom gstore ∪ ginval ∧ remove-refsize0(gstore0) = gstore0; (s)%⊦ inv-index(istore, istore0) ↔ inv(istore) ∧ inv(istore0) ∧ istore0 ⊑ istore ∧ remove-refsize0(istore0) = istore0; (s)%⊦ inv-state(pstate, nx, gstore, istore, syn) ↔ ( pstate.journal? → nx ≠ [] ∧ pstate.lnum = nx.last ∧ pstate.lnum ∈ gstore) ∧ (pstate.index? → pstate.lnum ∈ istore) ∧ (pstate = unbuffered → syn); (s)% ⊦ ¬ readonly.journal?; (s)% ⊦ ¬ readonly.index?; (s)%⊦ btree-inv(rp, @(m0, m1, m2), istore, istore0, zh, fi, fi0) → m0 ∈ istore; (ss)