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Proof step 54 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, false, 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, @(m1, m2, m3), height, false, ri, nodes(istore2) | alladrs1, alladrs1, alladrs1, ok) * true))(zh0), inv(indexblock(indx, lax, m4)), inv(istore2), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), refsize-cons(istore2, alladrs1), refsize-cons(istore, as), refsize-cons(istore0, alladrs0), m1 ∈ istore2, @(m1, m2, m3) ∈ istore2, @(m1, m2, m3) ∈ alladrs1, adr1 ∈ istore2, r0 ∈ zh0, m ∈ istore, adr1 ∈ istore, r0 ∈ zh, m ∈ istore2, m6 ∈ istore2, alladrs1 ∩ dom nodes(istore) ⊆ alladrs, alladrs1 ⊆ dom nodes(istore2), alladrs1 ∩ dom nodes(istore) ⊆ as, as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs ⊆ dom nodes(istore), istore ⊑ istore2, istore0 ⊑ istore2, istore0 ⊑ istore, height = 0 → alladrs1 = ∅ ++ @(m1, m2, m3), height = 0 → as = ∅ ⊦ # alladrs1 = 0, alladrs1 = ∅, dups(nx), adr1 ∈ as, (alladrs1 -- @(m1, m2, m3)) ++ adr1 ⊆ dom nodes(istore2)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
istore2[m1] = indexblock(indx, lax, m4), zh[r0] = mkznode(r, zbrar, boolvar, true, m0), istore[adr1] = istore2[adr1], zh0[r0] = mkznode(r1, zbrar0, boolvar0, false, 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, @(m1, m2, m3), height, false, ri, nodes(istore2) | alladrs1, alladrs1, alladrs1, ok) * true))(zh0), inv(indexblock(indx, lax, m4)), inv(istore2), inv(gstore \ ginval), inv(gstore0), inv(istore), inv(istore0), refsize-cons(istore2, alladrs1), refsize-cons(istore, as), refsize-cons(istore0, alladrs0), m1 ∈ istore2, @(m1, m2, m3) ∈ istore2, @(m1, m2, m3) ∈ alladrs1, adr1 ∈ istore2, r0 ∈ zh0, m ∈ istore, adr1 ∈ istore, r0 ∈ zh, m ∈ istore2, m6 ∈ istore2, alladrs1 ∩ dom nodes(istore) ⊆ alladrs, alladrs1 ⊆ dom nodes(istore2), alladrs1 ∩ dom nodes(istore) ⊆ as, as ⊆ alladrs, as ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore), alladrs0 ⊆ dom nodes(istore0), alladrs ⊆ dom nodes(istore), istore ⊑ istore2, istore0 ⊑ istore2, istore0 ⊑ istore ⊦ # alladrs1 = 0, alladrs1 = ∅, height = 0, dups(nx), adr1 ∈ as, (alladrs1 -- @(m1, m2, m3)) ++ adr1 ⊆ alladrs1, (alladrs1 -- @(m1, m2, m3)) ++ adr1 ⊆ dom nodes(istore2)

Rule argument

Additional information

Used simplifier rules: ⊦ adr ∈ nodes(istore) ↔ adr ∈ istore; (s)% ⊦ adr ∈ dom iast ↔ adr ∈ iast; (s)% ⊦ ∅ ++ adr ⊆ as ↔ adr ∈ as; (s)% ⊦ as = ∅ ++ adr → as -- adr = ∅; (s)% ⊦ {adr} = ∅ ++ adr; (s)%btree-dirty-adr-notin: ⊦ r ∈ zh ∧ zh[r] = mkznode(rp0, zbrar, boolvar, true, height0) ∧ (( btree (rp, r, adr, height, dirty, ri, iast, as, alladrs, nstat) * P) )(zh) → ¬ adr ∈ as ∧ (height = 0 → as = ∅); (forward) from specification btree-inv%btree-clean-adr-in: ⊦ r ∈ zh ∧ zh[r] = mkznode(rp0, zbrar, boolvar, false, height0) ∧ (( btree (rp, r, adr, height, dirty, ri, iast, as, alladrs, nstat) * P) )(zh) → adr ∈ as ∧ (height = 0 → as = ∅ ++ adr); (forward) from specification btree-inv%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-leaf-adr: ⊦ ((btree(rp, r, adr, 0, dirty, ri, iast, as, alladrs, nstat) * P) )(zh) → alladrs = {adr} ; (forward) from specification btree-inv%sub-ntrans-01: ⊦ as ⊆ as0 ∧ ¬ as1 ⊆ as0 → ¬ as1 ⊆ as; (forward) from specification set-basic[node-store]