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Proof step 8 from proof unmodified-payload (previous step)

BRANCH_SIZE = # zbrar, iast[adr] = indexnode(brar, bv1, nused), indexnode(brar, bv1, nused) = save(mkznode(rp, zbrar, bv1, false, nused)), sorted(zbrar, 0, nused), adr ∈ iast, key ∈ payload(load(brar, 0, nused), 0, nused), key ∈ payload(zbrar, 0, nused), nused ≤ BRANCH_SIZE ⊦ payload(load(brar, 0, nused), 0, nused)[key] = payload(zbrar, 0, nused)[key]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
m + nused ≤ # zbrar ⊦ key ∈ payload(zbrar, m, nused) ↔ (∃ n. n < nused ∧ zbrar[m + n].entry? ∧ zbrar[m + n].key = key)
Proof step 10:
BRANCH_SIZE = # zbrar, iast[adr] = indexnode(brar, bv1, nused), indexnode(brar, bv1, nused) = save(mkznode(rp, zbrar, bv1, false, nused)), sorted(zbrar, 0, nused), key ∈ payload(load(brar, 0, nused), 0, nused), adr ∈ iast, nused ≤ BRANCH_SIZE, 0 + nused ≤ # zbrar, ∃ n. n < nused ∧ zbrar[0 + n].entry? ∧ zbrar[0 + n].key = key ⊦ payload(load(brar, 0, nused), 0, nused)[key] = payload(zbrar, 0, nused)[key]

Rule argument

spec: <toplevel> name: in-payload seq: m + nused ≤ # zbrar ⊦ key ∈ payload(zbrar, m, nused) ↔ (∃ n. n < nused ∧ zbrar[m + n].entry? ∧ zbrar[m + n].key = key) subst: [nused, m, zbrar, key] → [nused, 0, zbrar, key] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ m < n → n ≠ 0; (s)% ⊦ ¬ n < n; (s) Used terms: nused, 0, zbrar, key