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Proof step 27 from proof btree-ri-unique (previous step)

# asar = # asar0, # zbrar0 = BRANCH_SIZE, # asar0 = m + 1, adr ∈ as1 ↔ ¬ dirty1, adr ∈ as0 ↔ adr ∈ as1, union(asar0, 0, # asar0) = alladrs1 -- adr, union(asar, 0, # asar0) = as1 -- adr, (( ( (λ n. ⌜zbrar0[n].branch?⌝ ∧ btree(rp0, zbrar0[n].child, zbrar0[n].adr, height0, dirty1, key-range(zbrar0, n, # asar0, ri1), iast, asar[n], asar0[n], ok) )⊗_ (0, # asar0 ) * rp0 => mkznode(rp, zbrar0, false, dirty1, # asar0)) * P1) )(zh), (( rp0 => mkznode(rp, zbrar0, false, dirty1, # asar0) * bnode(rp0, zbrar0, 0, # asar0, # asar0, height0 + 1, dirty1, ri0, iast, as0 -- adr, alladrs0 -- adr) * P0) )(zh), # asar0 < BRANCH_SIZE, disj(asar0, 0, # asar0), disj(asar, 0, # asar0), sorted(zbrar0, 0, m), unmodified(adr, mkznode(rp, zbrar0, false, dirty1, # asar0), iast), adr ∈ alladrs0, adr ∈ alladrs1, as0 ⊆ alladrs0, as0 ⊆ dom iast, as1 ⊆ alladrs1, as1 ⊆ dom iast, dirty1 → dirty, ∀ rp, rp0, adr, dirty, ri0, iast, as0, alladrs0, P0, zh, ri1, as1, alladrs1, P1. ((btree(rp, rp0, adr, height0, dirty, ri0, iast, as0, alladrs0, ok) * P0))(zh) ∧ ((btree(rp, rp0, adr, height0, dirty, ri1, iast, as1, alladrs1, ok) * P1))(zh) ∧ as0 ⊆ alladrs0 ∧ as0 ⊆ dom iast ∧ as1 ⊆ alladrs1 ∧ as1 ⊆ dom iast → ri0 = ri1 ∨ rp0 = null ⊦ # asar0 = 0, # alladrs1 = 0, # alladrs0 = 0, alladrs0 = ∅, alladrs1 = ∅, ri0 = ri1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
# asar = m + 1, # zbrar0 = BRANCH_SIZE, # asar0 = m + 1, adr ∈ as1 ↔ ¬ dirty1, adr ∈ as0 ↔ adr ∈ as1, union(asar0, 0, m + 1) = alladrs1 -- adr, union(asar, 0, m + 1) = as1 -- adr, (( ( (λ n. ⌜zbrar0[n].branch?⌝ ∧ btree(rp0, zbrar0[n].child, zbrar0[n].adr, height0, dirty1, key-range(zbrar0, n, m + 1, ri1), iast, asar[n], asar0[n], ok) )⊗_ (0, m + 1 ) * rp0 => mkznode(rp, zbrar0, false, dirty1, m + 1)) * P1) )(zh), (( rp0 => mkznode(rp, zbrar0, false, dirty1, m + 1) * bnode(rp0, zbrar0, 0, m + 1, m + 1, height0 + 1, dirty1, ri0, iast, as0 -- adr, alladrs0 -- adr) * P0) )(zh), m + 1 < BRANCH_SIZE, disj(asar0, 0, m + 1), disj(asar, 0, m + 1), sorted(zbrar0, 0, m), unmodified(adr, mkznode(rp, zbrar0, false, dirty1, m + 1), iast), adr ∈ alladrs0, adr ∈ alladrs1, as0 ⊆ alladrs0, as0 ⊆ dom iast, as1 ⊆ alladrs1, as1 ⊆ dom iast, dirty1 → dirty, ∀ rp, rp0, adr, dirty, ri0, iast, as0, alladrs0, P0, zh, ri1, as1, alladrs1, P1. ((btree(rp, rp0, adr, height0, dirty, ri0, iast, as0, alladrs0, ok) * P0))(zh) ∧ ((btree(rp, rp0, adr, height0, dirty, ri1, iast, as1, alladrs1, ok) * P1))(zh) ∧ as0 ⊆ alladrs0 ∧ as0 ⊆ dom iast ∧ as1 ⊆ alladrs1 ∧ as1 ⊆ dom iast → ri0 = ri1 ∨ rp0 = null ⊦ # alladrs1 = 0, # alladrs0 = 0, alladrs0 = ∅, alladrs1 = ∅, ri0 = ri1

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic