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Proof step 15 from proof btree-inv-format (previous step)

⊦ ∃ r, zh0, zbrar, nused. nused < BRANCH_SIZE ∧ unmodified (@(n, m0, m1), mkznode(null, zbrar, true, false, nused), nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)])) ∧ nused ≤ # zbrar ∧ # zbrar = BRANCH_SIZE ∧ sorted(zbrar, 0, nused) ∧ ((⌜∅ = payload(zbrar, 0, nused)⌝ * r => mkznode(null, zbrar, true, false, nused)))(zh0)

User applied rule apply lemma

And obtained the following new goals

Proof step 16:
⊦ ∃ r. r ≠ null ∧ ¬ r ∈ zh
Proof step 17:
∃ r. r ≠ null ∧ ¬ r ∈ ∅ ⊦ ∃ r, zh0, zbrar, nused. nused < BRANCH_SIZE ∧ unmodified (@(n, m0, m1), mkznode(null, zbrar, true, false, nused), nodes((∅)[n, indexblock(indexnode(mkbrarray(BRANCH_SIZE), true, 0) ', @(m0, m1) ', m1)])) ∧ nused ≤ # zbrar ∧ # zbrar = BRANCH_SIZE ∧ sorted(zbrar, 0, nused) ∧ ((⌜∅ = payload(zbrar, 0, nused)⌝ * r => mkznode(null, zbrar, true, false, nused)))(zh0)

Rule argument

spec: <toplevel> name: infinite-memory seq: ⊦ ∃ r. r ≠ null ∧ ¬ r ∈ zh subst: [zh] → [∅]

Additional information

Used terms: ∅