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Proof step 39 from proof btree-write-node (previous step)

# zbrar = BRANCH_SIZE, # asar = m + 1, # asar0 = m + 1, (( ( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r, zbrar[n].child, zbrar[n].adr, height0, true, key-range(zbrar, n, m + 1, ri), iast, asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * r => mkznode(r0, zbrar, false, true, m + 1)) * P) )(zh), m < BRANCH_SIZE, n < BRANCH_SIZE, btree-sub-clean(r, m + 1, zh), disj(asar, 0, m + 1), disj(asar0, 0, m + 1), nsize(m + 1, nstat), sorted(zbrar, 0, m), adr1 ∈ asar[n], n ≤ m, ∀ n. ¬ m < n → asar[n] ⊆ union(asar0, 0, m + 1) ++ adr0, ∀ n. ¬ m < n → asar[n] ⊆ dom iast ⊦ # asar[n] = 0, # union(asar, 0, m + 1) = 0, asar[n] = ∅, union(asar, 0, m + 1) = ∅, adr1 ∈ union(asar0, 0, m + 1), adr1 ∈ iast, adr0 ∈ union(asar0, 0, m + 1), adr0 ∈ union(asar, 0, m + 1)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 15 terms: n

Additional information

Used simplifier rules: ⊦ m ≤ n → (n < m ↔ false); (s)%sub-in: ⊦ adr ∈ as ∧ as ⊆ as0 → adr ∈ as0; (forward) from specification set-basic[node-store]% ⊦ adr ∈ dom iast ↔ adr ∈ iast; (s) Used terms: n