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Proof step 35 from proof btree-mark-dirty (previous step)

# asar0 = m + 1, # asar = m + 1, # zbrar = BRANCH_SIZE, zh[r] = mkznode(rp0, zbrar, false, false, m + 1), union(asar0, 0, m + 1) = alladrs -- adr, union(asar, 0, m + 1) = alladrs -- adr, (( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r, zbrar[n].child, zbrar[n].adr, height1, false, key-range(zbrar, n, m + 1, ri), iast, asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * P) )(zh -- r), m < BRANCH_SIZE, disj(asar0, 0, m + 1), disj(asar, 0, m + 1), nsize(m + 1, nstat), sorted(zbrar, 0, m), unmodified(adr, mkznode(rp0, zbrar, false, false, m + 1), iast), adr ∈ alladrs, adr ∈ iast, r ∈ zh, alladrs ⊆ dom iast, ∀ zh, r, rp0, zbrar, boolvar, height0, rp, adr, ri, iast, alladrs, nstat, P. zh[r] = mkznode(rp0, zbrar, boolvar, false, height0) ∧ ((btree(rp, r, adr, height1, false, ri, iast, alladrs, alladrs, nstat) * P))(zh) ∧ r ∈ zh ∧ adr ∈ alladrs ∧ adr ∈ iast ∧ alladrs ⊆ dom iast ∧ (height1 = 0 → alladrs = ∅ ++ adr) → # alladrs = 0 ∨ alladrs = ∅ ∨ ((btree(rp, r, adr, height1, true, ri, iast, alladrs -- adr, alladrs, nstat) * P))(zh[r, mkznode(rp0, zbrar, boolvar, true, height0)]) ⊦ # alladrs = 0, alladrs = ∅, ∃ asar1. # asar1 = m + 1 ∧ disj(asar1, 0, m + 1) ∧ union(asar1, 0, m + 1) = alladrs -- adr ∧ (∃ asar2. # asar2 = m + 1 ∧ disj(asar2, 0, m + 1) ∧ union(asar2, 0, m + 1) = alladrs -- adr ∧ (( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r, zbrar[n].child, zbrar[n].adr, height1, true, key-range(zbrar, n, m + 1, ri), iast, asar1[n], asar2[n], ok) )⊗_ (0, m + 1 ) * P) )(zh -- r))

User applied rule exists right

And obtained the following new goals

Proof step 36:
# zbrar = BRANCH_SIZE, # asar = m + 1, # asar0 = m + 1, zh[r] = mkznode(rp0, zbrar, false, false, m + 1), union(asar, 0, m + 1) = alladrs -- adr, union(asar0, 0, m + 1) = alladrs -- adr, (( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r, zbrar[n].child, zbrar[n].adr, height1, false, key-range(zbrar, n, m + 1, ri), iast, asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * P) )(zh -- r), m < BRANCH_SIZE, disj(asar, 0, m + 1), disj(asar0, 0, m + 1), nsize(m + 1, nstat), sorted(zbrar, 0, m), unmodified(adr, mkznode(rp0, zbrar, false, false, m + 1), iast), r ∈ zh, adr ∈ iast, adr ∈ alladrs, alladrs ⊆ dom iast, ∀ zh, r, rp0, zbrar, boolvar, height0, rp, adr, ri, iast, alladrs, nstat, P. zh[r] = mkznode(rp0, zbrar, boolvar, false, height0) ∧ ((btree(rp, r, adr, height1, false, ri, iast, alladrs, alladrs, nstat) * P))(zh) ∧ r ∈ zh ∧ adr ∈ alladrs ∧ adr ∈ iast ∧ alladrs ⊆ dom iast ∧ (height1 = 0 → alladrs = ∅ ++ adr) → # alladrs = 0 ∨ alladrs = ∅ ∨ ((btree(rp, r, adr, height1, true, ri, iast, alladrs -- adr, alladrs, nstat) * P))(zh[r, mkznode(rp0, zbrar, boolvar, true, height0)]) ⊦ # alladrs = 0, alladrs = ∅, # asar = m + 1 ∧ disj(asar, 0, m + 1) ∧ union(asar, 0, m + 1) = alladrs -- adr ∧ (∃ asar2. # asar2 = m + 1 ∧ disj(asar2, 0, m + 1) ∧ union(asar2, 0, m + 1) = alladrs -- adr ∧ (( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r, zbrar[n].child, zbrar[n].adr, height1, true, key-range(zbrar, n, m + 1, ri), iast, asar[n], asar2[n], ok) )⊗_ (0, m + 1 ) * P) )(zh -- r))

Rule argument

pos: right 3 terms: asar abort: F discard: T computed: T

Additional information

Used terms: asar