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Proof step 13 from proof btree-clean-alladrs (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
# zbrar = BRANCH_SIZE, # asar = # asar0, # asar0 = m + 1, union(asar, 0, # asar0) = as -- adr, union(asar0, 0, # asar0) = alladrs -- adr, (( ( (λ n. ⌜zbrar[n].branch?⌝ ∧ btree(r0, zbrar[n].child, zbrar[n].adr, height0, false, key-range(zbrar, n, # asar0, ri), iast, asar[n], asar0[n], ok) )⊗_ (0, # asar0 ) * r0 => mkznode(rp, zbrar, false, false, # asar0)) * P) )(zh0), disj(asar, 0, # asar0), disj(asar0, 0, # asar0), nsize(# asar0, nstat), sorted(zbrar, 0, m), unmodified(adr, mkznode(rp, zbrar, false, false, # asar0), iast), adr ∈ as, adr ∈ alladrs, adr ∈ iast, # asar0 ≤ BRANCH_SIZE, as ⊆ alladrs, as ⊆ dom iast, (r = null ⊃ P(zh);r0 = r ∧ zh0 = zh), ∀ rp, r, adr, ri, iast, as, alladrs, nstat, P, zh. ((btree(rp, r, adr, height0, false, ri, iast, as, alladrs, nstat) * P))(zh) → as = alladrs ⊦ # as = 0, # alladrs = 0, # asar0 = 0, alladrs = ∅, as = ∅, as = alladrs

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [# asar0, m]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: # asar0, m