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Proof step 17 from proof inv-commit-rec (previous step)

zh[r0] = mkznode(r, zbrar, boolvar, true, m0), istore[adr1] = istore2[adr1], remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ((btree(null, r0, (err = ESUCCESS ⊃ @(m1, m2, m3);adr1), height, err ≠ ESUCCESS, ri, nodes(istore2) | as0, as0, alladrs1, ok) * true))(zh0), ((btree(null, r0, adr1, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh), ((btree(null, null, adr1, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh), ((btree(null, r0, adr1, height, dirty, ri, nodes(istore) | as, as, alladrs, ok) * true))(zh), inv(istore2), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), refsize-cons(istore2, as0), refsize-cons(istore, as), refsize-cons(istore0, alladrs0), adr1 ∈ istore2, r0 ∈ zh0, m ∈ istore, adr1 ∈ istore, r0 ∈ zh, m ∈ istore2, as0 ⊆ dom nodes(istore2), as0 ⊆ alladrs1, as0 ∩ dom nodes(istore) ⊆ as, alladrs1 ⊆ alladrs ∪ as0, as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs ⊆ dom nodes(istore), as0 ∩ dom nodes(istore) ⊆ alladrs, istore ⊑ istore2, istore0 ⊑ istore2, istore0 ⊑ istore, pstate0.journal? → nx ≠ [] ∧ pstate0.lnum = nx.last ∧ pstate0.lnum ∈ gstore, pstate0.index? → pstate0.lnum ∈ istore2, pstate0 = unbuffered → bv, err = ESUCCESS → ¬ zh0[r0].dirty ∧ pstate0.index?, height = 0 → as = ∅ ⊦ dups(nx), adr1 ∈ as, (err ≠ ESUCCESS → btree-inv(r0, adr1, istore2, istore0, zh0, ri, fi)) ∧ ( err = ESUCCESS → btree-inv(r0, @(m1, m2, m3), istore2, istore2, zh0, ri, ri) ∧ btree-inv(r0, adr1, istore2[m1, istore2[m1].ref-size:= (istore2[m1].ref-size - m3)], istore0, zh0[r0, zh0[r0].dirty:= true], ri, fi) ∧ ¬ zh0[r0].dirty)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
istore[adr1] = istore2[adr1], zh[r0] = mkznode(r, zbrar, boolvar, true, m0), istore2[m1] = indexblock(indx, lax, m4), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ((btree(null, r0, adr1, height, dirty, ri, nodes(istore) | as, as, alladrs, ok) * true))(zh), ((btree(null, null, adr1, height0, false, fi, nodes(istore0), alladrs0, alladrs0, ok) * true))(zh), ((btree(null, r0, adr1, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh), ((btree(null, r0, (err = ESUCCESS ⊃ @(m1, m2, m3);adr1), height, err ≠ ESUCCESS, ri, nodes(istore2) | as0, as0, alladrs1, ok) * true))(zh0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(istore2), refsize-cons(istore0, alladrs0), refsize-cons(istore, as), refsize-cons(istore2, as0), m ∈ istore2, r0 ∈ zh, adr1 ∈ istore, m ∈ istore, r0 ∈ zh0, adr1 ∈ istore2, as0 ∩ dom nodes(istore) ⊆ alladrs, alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs0 ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs, alladrs1 ⊆ alladrs ∪ as0, as0 ∩ dom nodes(istore) ⊆ as, as0 ⊆ alladrs1, as0 ⊆ dom nodes(istore2), istore0 ⊑ istore, istore0 ⊑ istore2, istore ⊑ istore2, height = 0 → as = ∅, err = ESUCCESS → ¬ zh0[r0].dirty ∧ pstate0.index?, pstate0 = unbuffered → bv, pstate0.index? → pstate0.lnum ∈ istore2, pstate0.journal? → nx ≠ [] ∧ pstate0.lnum = nx.last ∧ pstate0.lnum ∈ gstore ⊦ dups(nx), adr1 ∈ as, (err ≠ ESUCCESS → btree-inv(r0, adr1, istore2, istore0, zh0, ri, fi)) ∧ ( err = ESUCCESS → btree-inv(r0, @(m1, m2, m3), istore2, istore2, zh0, ri, ri) ∧ btree-inv(r0, adr1, istore2[m1, istore2[m1].ref-size:= (m4 - m3)], istore0, zh0[r0, zh0[r0].dirty:= true], ri, fi) ∧ ¬ zh0[r0].dirty)

Rule argument

spec: ablock, inst: index-store name: elim seq: ⊦ (indx = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indx, lax, m) subst: [iblock, indx, lax, m] → [istore2[m1], indx, lax, m4]

Additional information

Used simplifier rules: ⊦ (indx = iblock.indlist ∧ lax = iblock.ladrlist) ∧ m = iblock.ref-size ↔ iblock = indexblock(indx, lax, m); (elim) Used terms: istore2[m1], indx, lax, m4