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Proof step 59 from proof inv-commit-rec (previous step)

istore2[m1] = indexblock(indx, lax, m4), zh[r0] = mkznode(r, zbrar, boolvar, true, m0), istore[adr1] = istore2[adr1], zh0[r0] = mkznode(r1, zbrar0, boolvar0, boolvar1, m5), remove-refsize0(gstore0) = gstore0, remove-refsize0(istore0) = istore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ((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, adr1, height, true, ri, nodes(istore2) | as0, as0, alladrs1, ok) * true))(zh0), 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, height = 0 → as = ∅ ⊦ err = ESUCCESS, btree-inv(r0, adr1, istore2, istore0, zh0, ri, fi), dups(nx), adr1 ∈ as

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 60:
⊦ btree-inv(r, adr, istore, istore0, zh, ri, fi) ↔ (∃ height, dirty, as, alladrs. ((btree(null, r, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true))(zh) ∧ refsize-cons(istore, as) ∧ adr ∈ istore ∧ alladrs ⊆ dom nodes(istore)) ∧ (∃ height, dirty, as, alladrs. ((btree(null, null, adr, height, false, fi, nodes(istore0), as, alladrs, ok) * true))(zh) ∧ refsize-cons(istore0, as) ∧ alladrs ⊆ dom nodes(istore))
Proof step 61:
zh0[r0] = mkznode(r1, zbrar0, boolvar0, boolvar1, m5), 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, true, 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), 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 = ∅, pstate0 = unbuffered → bv, pstate0.index? → pstate0.lnum ∈ istore2, pstate0.journal? → nx ≠ [] ∧ pstate0.lnum = nx.last ∧ pstate0.lnum ∈ gstore ⊦ err = ESUCCESS, dups(nx), adr1 ∈ as, (∃ height, dirty, as, alladrs. ((btree(null, r0, adr1, height, dirty, ri, nodes(istore2), as, alladrs, ok) * true))(zh0) ∧ refsize-cons(istore2, as) ∧ adr1 ∈ istore2 ∧ alladrs ⊆ dom nodes(istore2)) ∧ (∃ height, dirty, as, alladrs. ((btree(null, null, adr1, height, false, fi, nodes(istore0), as, alladrs, ok) * true))(zh0) ∧ refsize-cons(istore0, as) ∧ alladrs ⊆ dom nodes(istore2))

Rule argument

spec: btree-inv name: btree-inv seq: ⊦ btree-inv(r, adr, istore, istore0, zh, ri, fi) ↔ (∃ height, dirty, as, alladrs. (( btree (null, r, adr, height, dirty, ri, nodes(istore), as, alladrs, ok) * true) )(zh) ∧ refsize-cons(istore, as) ∧ adr ∈ istore ∧ alladrs ⊆ dom nodes(istore)) ∧ (∃ height, dirty, as, alladrs. (( btree (null, null, adr, height, false, fi, nodes(istore0), as, alladrs, ok) * true) )(zh) ∧ refsize-cons(istore0, as) ∧ alladrs ⊆ dom nodes(istore)) subst: [fi, ri, zh, istore0, istore, adr, r] → [fi, ri, zh0, istore0, istore2, adr1, r0] flags: <all paths>

Additional information

Used terms: fi, ri, zh0, istore0, istore2, adr1, r0