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Proof step 50 from proof inv-commit-rec (previous step)

istore[adr1] = istore2[adr1], zh[r0] = mkznode(r, zbrar, boolvar, true, m0), istore2[m1] = indexblock(indx, lax, m4), zh0[r0] = mkznode(r1, zbrar0, boolvar0, false, m5), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ((btree(null, r0, @(m1, m2, m3), height, false, ri, nodes(istore2) | alladrs1, alladrs1, 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, @(m1, m2, m3), height, false, ri, nodes(istore2), alladrs1, alladrs1, ok) * true))(zh0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(istore2), inv(indexblock(indx, lax, m4)), refsize-cons(istore0, alladrs0), refsize-cons(istore, as), refsize-cons(istore2, alladrs1), m6 ∈ istore2, m ∈ istore2, r0 ∈ zh, adr1 ∈ istore, m ∈ istore, adr1 ∈ istore2, @(m1, m2, m3) ∈ alladrs1, @(m1, m2, m3) ∈ istore2, m1 ∈ istore2, r0 ∈ zh0, alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs0 ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs, alladrs1 ∩ dom nodes(istore) ⊆ as, alladrs1 ⊆ dom nodes(istore2), alladrs1 ∩ dom nodes(istore) ⊆ alladrs, istore0 ⊑ istore, istore0 ⊑ istore2, istore ⊑ istore2, height = 0 → as = ∅, height = 0 → alladrs1 = ∅ ++ @(m1, m2, m3) ⊦ # alladrs1 = 0, alladrs1 = ∅, ((btree(null, r0, adr1, height, true, ri, nodes(istore2), alladrs1 -- @(m1, m2, m3), (alladrs1 -- @(m1, m2, m3)) ++ adr1, ok) * true) )(zh0[r0, mkznode(r1, zbrar0, boolvar0, true, m5)]), dups(nx), adr1 ∈ as, ¬ adr1 ∈ alladrs1 ∧ true

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
istore[adr1] = istore2[adr1], zh[r0] = mkznode(r, zbrar, boolvar, true, m0), istore2[m1] = indexblock(indx, lax, m4), zh0[r0] = mkznode(r1, zbrar0, boolvar0, false, m5), remove-refsize0(istore0) = istore0, remove-refsize0(gstore0) = gstore0, elems nx ∩ ginval = ∅, dom gstore0 ∪ elems nx = dom gstore ∪ ginval, ((btree(null, r0, @(m1, m2, m3), height, false, ri, nodes(istore2) | alladrs1, alladrs1, 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, @(m1, m2, m3), height, false, ri, nodes(istore2), alladrs1, alladrs1, ok) * true))(zh0), inv(istore0), inv(istore), inv(gstore0), inv(gstore \ ginval), inv(istore2), inv(indexblock(indx, lax, m4)), refsize-cons(istore0, alladrs0), refsize-cons(istore, as), refsize-cons(istore2, alladrs1), adr1 ∈ alladrs1, m6 ∈ istore2, m ∈ istore2, r0 ∈ zh, adr1 ∈ istore, m ∈ istore, @(m1, m2, m3) ∈ alladrs1, @(m1, m2, m3) ∈ istore2, m1 ∈ istore2, r0 ∈ zh0, adr1 ∈ istore2, alladrs1 ⊆ dom nodes(istore2), alladrs ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs0 ⊆ dom nodes(istore), as ⊆ dom nodes(istore), as ⊆ alladrs, alladrs1 ∩ dom nodes(istore) ⊆ as, alladrs1 ∩ dom nodes(istore) ⊆ alladrs, istore0 ⊑ istore, istore0 ⊑ istore2, istore ⊑ istore2, height = 0 → as = ∅, height = 0 → alladrs1 = ∅ ++ @(m1, m2, m3) ⊦ # alladrs1 = 0, alladrs1 = ∅, ((btree(null, r0, adr1, height, true, ri, nodes(istore2), alladrs1 -- @(m1, m2, m3), (alladrs1 -- @(m1, m2, m3)) ++ adr1, ok) * true) )(zh0[r0, mkznode(r1, zbrar0, boolvar0, true, m5)]), dups(nx), adr1 ∈ as

Rule argument

Additional information

Used simplifier rules: ⊦ adr ∈ nodes(istore) ↔ adr ∈ istore; (s)% ⊦ adr ∈ dom iast ↔ adr ∈ iast; (s)%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]%btree-adrs: ⊦ (( btree (rp, rp0, adr0, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ dom iast; (forward) from specification btree-inv%sub-in: ⊦ adr ∈ as ∧ as ⊆ as0 → adr ∈ as0; (forward) from specification set-basic[node-store]