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Proof step 38 from proof btree-write-other (previous step)

# zbrar = BRANCH_SIZE, # asar = m + 1, # asar0 = m + 1, adr0 ∈ as ↔ ¬ dirty0, union(asar, 0, m + 1) = as -- adr0, union(asar0, 0, m + 1) = alladrs -- adr0, (( ( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r0, zbrar[n].child, zbrar[n].adr, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast[adr, ind], asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * r0 => mkznode(rp, zbrar, false, dirty0, m + 1)) * P) )(zh0), m < BRANCH_SIZE, disj(asar, 0, m + 1), disj(asar0, 0, m + 1), nsize(m + 1, nstat), sorted(zbrar, 0, m), unmodified(adr0, mkznode(rp, zbrar, false, dirty0, m + 1), iast[adr, ind]), adr0 ∈ alladrs, dirty0 → dirty, (r = null ⊃ adr0 ∈ as ∧ P(zh);r0 = r ∧ zh0 = zh), ∀ rp, r, adr0, dirty, ri, iast, adr, ind, as, alladrs, nstat, P, zh. ( ((btree(rp, r, adr0, height0, dirty, ri, iast[adr, ind], as, alladrs, nstat) * P))(zh) ↔ ((btree(rp, r, adr0, height0, dirty, ri, iast, as, alladrs, nstat) * P))(zh)) ∨ adr ∈ as ⊦ # alladrs = 0, alladrs = ∅, (( ( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r0, zbrar[n].child, zbrar[n].adr, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast, asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * r0 => mkznode(rp, zbrar, false, dirty0, m + 1)) * P) )(zh0), adr ∈ as, (∀ n0, P. n0 < m + 1 ∧ (( ( ⌜zbrar[0 + n0].branch?⌝ ∧ btree (r0, zbrar[0 + n0].child, zbrar[0 + n0].adr, height0, dirty0, key-range(zbrar, 0 + n0, m + 1, ri), iast[adr, ind], asar[0 + n0], asar0[0 + n0], ok)) * P) )(zh0) → (( ( ⌜zbrar[0 + n0].branch?⌝ ∧ btree (r0, zbrar[0 + n0].child, zbrar[0 + n0].adr, height0, dirty0, key-range(zbrar, 0 + n0, m + 1, ri), iast, asar[0 + n0], asar0[0 + n0], ok)) * P) )(zh0)) ∧ (( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r0, zbrar[n].child, zbrar[n].adr, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast[adr, ind], asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * P * r0 => mkznode(rp, zbrar, false, dirty0, m + 1)) )(zh0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: btree-refed-subseteq-alladrs: ⊦ (( btree(rp, r, adr, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ alladrs;%btree-adrs: ⊦ (( btree (rp, rp0, adr0, height, dirty, fi, iast, as, alladrs, nstat) * P) )(zh) → as ⊆ dom iast;%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%dom-ins: ⊦ dom iast[adr, ind] = dom iast ++ adr; from specification store+set[index-store-address-store]%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat%true-and: ⊦ (true ∧ P0) = P0; from specification heap-sep[zheap]%true-rev: ⊦ ⌜true⌝ = true; from specification heap-sep[zheap]%prop: ⊦ ⌜bv⌝ (zh) ↔ bv; from specification heap-sep[zheap]%and: ⊦ ((P ∧ P2))(zh) ↔ ¬ ¬(P(zh) ∧ P2(zh)); 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]%and-com: ⊦ (P ∧ P2) = (P2 ∧ P); from specification heap-sep[zheap]%and-ass: ⊦ ((P ∧ P3) ∧ P4) = (P ∧ P3 ∧ P4); from specification heap-sep[zheap]%prop-shift: ⊦ (⌜bv⌝ ∧ P) * P2 = (⌜bv⌝ ∧ P * P2); from specification heap-sep[zheap]%add-base: ⊦ n + 0 = n; from specification nat-basic2%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%s: ⊦ m < n + 1 ↔ ¬ n < m; from specification nat-basic2