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Proof step 36 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, 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 ∈ union(asar, 0, m + 1), ∀ n. ¬ m < n → asar[n] ⊆ union(asar0, 0, m + 1) ++ adr0, ∀ n. ¬ m < n → asar[n] ⊆ dom iast ⊦ # union(asar, 0, m + 1) = 0, 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)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: address-set-array-ops name: in-union-ext seq: ⊦ adr ∈ union(asar, n, m) ↔ (∃ n0. n ≤ n0 ∧ n0 < n + m ∧ adr ∈ asar[n0]) subst: [m, n, asar, adr] → [m + 1, 0, asar, adr1] flags: <all paths>

Additional information

Used terms: m + 1, 0, asar, adr1