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Proof step 12 from proof btree-write-node (previous step)

zh[r] = mkznode(r0, zbrar, boolvar, true, m0), height = height0 +1, ((btree(rp, r, adr0, height, dirty, ri, iast, as, alladrs, nstat) * P))(zh), btree-sub-clean(r, m0, zh), r ∈ zh, as ⊆ alladrs, as ⊆ dom iast, height = 0 → as = ∅ ⊦ ((btree(rp, r, adr1, height, false, ri, iast[adr1, save(mkznode(r0, zbrar, boolvar, true, m0))], as ++ adr1, (alladrs -- adr0) ++ adr1, nstat) * P) )(zh[r, mkznode(r0, zbrar, boolvar, false, m0)]), adr0 ∈ as, adr1 ∈ alladrs, adr1 ∈ iast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
zh[r] = mkznode(r0, zbrar, boolvar, true, m0), ((btree(rp, r, adr0, height0 + 1, dirty, ri, iast, as, alladrs, nstat) * P))(zh), btree-sub-clean(r, m0, zh), r ∈ zh, as ⊆ alladrs, as ⊆ dom iast ⊦ (( btree (rp, r, adr1, height0 + 1, false, ri, iast[adr1, save(mkznode(r0, zbrar, boolvar, true, m0))], as ++ adr1, (alladrs -- adr0) ++ adr1, nstat) * P) )(zh[r, mkznode(r0, zbrar, boolvar, false, m0)]), adr0 ∈ as, adr1 ∈ alladrs, adr1 ∈ iast

Rule argument

Additional information

Used simplifier rules: 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 = ∅);%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)% ⊦ m +1 = m + 1; (s)