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Proof step 50 from proof btree-istore-reduce-refed (previous step)

# zbrar = BRANCH_SIZE, # asar = m + 1, # asar0 = m + 1, adr ∈ as ↔ ¬ dirty0, zbrar[n] = mkzbranch(key, adr0, r0), union(asar, 0, m + 1) = as -- adr, union(asar0, 0, m + 1) = alladrs -- adr, ((btree(r, r0, adr0, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast0, asar[n], asar0[n], ok) * P0))(zh0), (( ( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r, zbrar[n].child, zbrar[n].adr, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast0, asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * r => mkznode(rp, zbrar, false, dirty0, m + 1)) * P) )(zh0), n < BRANCH_SIZE, m < BRANCH_SIZE, disj(asar, 0, m + 1), disj(asar0, 0, m + 1), nsize(m + 1, nstat), sorted(zbrar, 0, m), unmodified(adr, mkznode(rp, zbrar, false, dirty0, m + 1), iast0), adr ∈ alladrs, n ≤ m, asar[n] ⊆ asar0[n], asar[n] ⊆ dom iast0, as ⊆ alladrs, as ⊆ dom iast0, iast0 | as ⊆ iast1, dirty0 → dirty, (rp0 = null ⊃ adr ∈ as ∧ P(zh);r = rp0 ∧ zh0 = zh), ∀ rp, rp0, adr, dirty, ri, iast0, as, alladrs, nstat, P, zh, iast1. ((btree(rp, rp0, adr, height0, dirty, ri, iast0, as, alladrs, nstat) * P))(zh) ∧ iast0 | as ⊆ iast1 ∧ as ⊆ dom iast0 ∧ as ⊆ alladrs → ((btree(rp, rp0, adr, height0, dirty, ri, iast1, as, alladrs, nstat) * P))(zh) ⊦ # alladrs = 0, alladrs = ∅, ((btree(r, r0, adr0, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast1, asar[n], asar0[n], ok) * P0))(zh0), (( ( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r, zbrar[n].child, zbrar[n].adr, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast1, asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * r => mkznode(rp, zbrar, false, dirty0, m + 1)) * P) )(zh0)

User applied rule all left

And obtained the following new goals

Proof step 51:
# asar0 = m + 1, # asar = m + 1, # zbrar = BRANCH_SIZE, adr ∈ as ↔ ¬ dirty0, zbrar[n] = mkzbranch(key, adr0, r0), union(asar0, 0, m + 1) = alladrs -- adr, union(asar, 0, m + 1) = as -- adr, (( ( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r, zbrar[n].child, zbrar[n].adr, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast0, asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * r => mkznode(rp, zbrar, false, dirty0, m + 1)) * P) )(zh0), ((btree(r, r0, adr0, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast0, asar[n], asar0[n], ok) * P0))(zh0), m < BRANCH_SIZE, n < BRANCH_SIZE, disj(asar0, 0, m + 1), disj(asar, 0, m + 1), nsize(m + 1, nstat), sorted(zbrar, 0, m), unmodified(adr, mkznode(rp, zbrar, false, dirty0, m + 1), iast0), adr ∈ alladrs, n ≤ m, iast0 | as ⊆ iast1, as ⊆ dom iast0, as ⊆ alladrs, asar[n] ⊆ dom iast0, asar[n] ⊆ asar0[n], dirty0 → dirty, ((btree(r, r0, adr0, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast0, asar[n], asar0[n], ok) * P0))(zh0) ∧ iast0 | asar[n] ⊆ iast1 ∧ asar[n] ⊆ dom iast0 ∧ asar[n] ⊆ asar0[n] → ((btree(r, r0, adr0, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast1, asar[n], asar0[n], ok) * P0))(zh0), (rp0 = null ⊃ adr ∈ as ∧ P(zh);r = rp0 ∧ zh0 = zh) ⊦ # alladrs = 0, alladrs = ∅, (( ( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r, zbrar[n].child, zbrar[n].adr, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast1, asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * r => mkznode(rp, zbrar, false, dirty0, m + 1)) * P) )(zh0), ((btree(r, r0, adr0, height0, dirty0, key-range(zbrar, n, m + 1, ri), iast1, asar[n], asar0[n], ok) * P0))(zh0)

Rule argument

pos: left 26 terms: r, r0, adr0, dirty0, key-range(zbrar, n, m + 1, ri), iast0, asar[n], asar0[n], ok, P0, zh0, iast1 abort: F discard: T computed: T

Additional information

Used terms: r, r0, adr0, dirty0, key-range(zbrar, n, m + 1, ri), iast0, asar[n], asar0[n], ok, P0, zh0, iast1