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Proof step 8 from proof btree-write-other (previous step)

⊦ (∃ 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, 0 = 0, dirty1, nused), iast[adr, ind]) ∧ (( r1 => mkznode(rp, zbrar, 0 = 0, dirty1, nused) * bnode(r1, zbrar, 0, nused, nused, 0, dirty1, ri, iast[adr, ind], as -- adr0, alladrs -- adr0) * P) )(zh1)) ↔ (∃ r0, zh0, zbrar, dirty0, nused. (r = null ⊃ ¬ dirty0 ∧ P(zh);r0 = r ∧ zh0 = zh) ∧ (dirty0 → dirty) ∧ (adr0 ∈ as ↔ ¬ dirty0) ∧ adr0 ∈ alladrs ∧ nsize(nused, nstat) ∧ unmodified(adr0, mkznode(rp, zbrar, true, dirty0, nused), iast) ∧ nused ≤ # zbrar ∧ # zbrar = BRANCH_SIZE ∧ sorted(zbrar, 0, nused) ∧ ri = payload(zbrar, 0, nused) ∧ as -- adr0 = ∅ ∧ alladrs -- adr0 = ∅ ∧ ((P * r0 => mkznode(rp, zbrar, true, dirty0, nused)))(zh0)), adr ∈ as

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: bleaf: ⊦ bnode(rp, zbrar, m, len, nused, 0, dirty, ri, iast, as, alladrs) = ( ⌜m + len ≤ nused ∧ nused ≤ # zbrar ∧ # zbrar = BRANCH_SIZE⌝ ∧ ⌜sorted(zbrar, 0, nused)⌝ ∧ ⌜ri = payload(zbrar, m, len)⌝ ∧ ⌜as = ∅⌝ ∧ ⌜alladrs = ∅⌝ ∧ emp);%prop: ⊦ ⌜bv⌝ (zh) ↔ bv; from specification heap-sep[zheap]%and: ⊦ ((P ∧ P2))(zh) ↔ ¬ ¬(P(zh) ∧ P2(zh)); from specification heap-sep[zheap]%and-com: ⊦ (P ∧ P2) = (P2 ∧ P); from specification heap-sep[zheap]%and-ass: ⊦ ((P ∧ P3) ∧ P4) = (P ∧ P3 ∧ P4); from specification heap-sep[zheap]%sep-com: ⊦ P * P2 = P2 * P; from specification heap-sep[zheap]%sep-ass: ⊦ (P * P3) * P4 = P * P3 * P4; from specification heap-sep[zheap]%emp-sep: ⊦ emp * P0 = P0; from specification heap-sep[zheap]%prop-shift: ⊦ (⌜bv⌝ ∧ P) * P2 = (⌜bv⌝ ∧ P * P2); from specification heap-sep[zheap]%ler: ⊦ m ≤ m; from specification nat%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%add-base: ⊦ n + 0 = n; from specification nat-basic2