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

zbrar[n + n0] = mkzentry(key, adr), n0 < nused, n + nused ≤ # zbrar, nused + n ≤ # zbrar ⊦ key ∈ keys(zbrar, n, nused)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
m + nused ≤ # zbrar ⊦ key ∈ keys(zbrar, m, nused) ↔ (∃ n. n < nused ∧ zbrar[m + n].key = key)
Proof step 10:
zbrar[n + n0] = mkzentry(key, adr), n0 < nused, nused + n ≤ # zbrar, n + nused ≤ # zbrar ⊦ ∃ n0. n0 < nused ∧ zbrar[n + n0].key = key

Rule argument

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

Additional information

Used terms: nused, n, zbrar, key