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Proof step 15 from proof btree-write-node (previous step)

zh[r] = mkznode(r0, zbrar, boolvar, true, m0), btree-sub-clean(r, m0, zh), r ∈ zh, as ⊆ dom iast, as ⊆ alladrs, ∃ r1, zh1, zbrar, dirty1, nused. (r = null ⊃ ¬ dirty1 ∧ P(zh);r1 = r ∧ zh1 = zh) ∧ (dirty1 → dirty) ∧ (adr0 ∈ as ↔ ¬ dirty1) ∧ adr0 ∈ alladrs ∧ nsize(nused, nstat) ∧ unmodified(adr0, mkznode(rp, zbrar, height0 + 1 = 0, dirty1, nused), iast) ∧ (( r1 => mkznode(rp, zbrar, height0 + 1 = 0, dirty1, nused) * bnode(r1, zbrar, 0, nused, nused, height0 + 1, dirty1, ri, iast, as -- adr0, alladrs -- adr0) * P) )(zh1) ⊦ (( 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)]), adr1 ∈ iast, adr1 ∈ alladrs, adr0 ∈ as

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
((r => mkznode(r0, zbrar, false, true, m0) * bnode(r, zbrar, 0, m0, m0, height0 + 1, true, ri, iast, as, alladrs -- adr0) * P))(zh), btree-sub-clean(r, m0, zh), nsize(m0, nstat), adr0 ∈ alladrs, as ⊆ alladrs, as ⊆ dom iast ⊦ # alladrs = 0, alladrs = ∅, (( btree(r0, r, adr1, height0 + 1, false, ri, iast[adr1, save(mkznode(r0, zbrar, false, true, m0))], as ++ adr1, (alladrs -- adr0) ++ adr1, nstat) * P) )(zh[r, mkznode(r0, zbrar, false, false, m0)]), adr0 ∈ as, adr1 ∈ alladrs, adr1 ∈ iast

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ as ≠ ∅ → # as ≠ 0; (forward) from specification set-basic[node-store]% ⊦ ((r => znd * P0))(zh) → r ∈ zh; (s)% ⊦ unmodified(adr, mkznode(rp, zbrar, bv, true, nused), iast); (s)%⊦ mkznode(r, zbrar, boolvar, boolvar0, m) = mkznode(r0, zbrar0, boolvar1, boolvar2, m0) ↔ r = r0 ∧ zbrar = zbrar0 ∧ (boolvar ↔ boolvar1) ∧ (boolvar0 ↔ boolvar2) ∧ m = m0; (ws)% ⊦ ((r => znd * P0))(zh) → (zh[r] = znd0 ↔ znd = znd0); (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]%ne-01: ⊦ adr ∈ as → as ≠ ∅; (forward) from specification set-basic[node-store]% ⊦ r ∈ zh → r ≠ null; (s)% ⊦ ¬ adr ∈ as → as -- adr = as; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)