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Proof step 42 from proof btree-write-node (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# zbrar = BRANCH_SIZE, # asar = m + 1, # asar0 = m + 1, zh[r] = mkznode(r0, zbrar, false, true, m + 1), (( P * (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 )) )(zh -- r), 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), r ∈ zh, ∀ n. ¬ m < n → asar[n] ⊆ union(asar0, 0, m + 1) ++ adr0, ∀ n. ¬ m < n → asar[n] ⊆ dom iast ⊦ adr1 = adr0, (( ( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree (r, zbrar[n].child, zbrar[n].adr, height0, false, key-range(zbrar, n, m + 1, ri), iast[adr1, save(mkznode(r0, zbrar, false, true, m + 1))], asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * r =>_) * P) )(zh), adr1 ∈ union(asar0, 0, m + 1), adr1 ∈ iast, adr0 ∈ union(asar0, 0, m + 1), adr0 ∈ union(asar, 0, m + 1)

Rule argument

Additional information

Used simplifier rules: ⊦ zh ≡ zh; (s)