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Proof step 38 from proof in-payload (previous step)

zbrar[m + n] = mkzentry(key, adr), m < # zbrar, m + nused0 < # zbrar, n ≤ nused0 ⊦ zbrar[m].entry?, key ∈ payload(zbrar, m + 1, nused0), ∃ n0. n0 < nused0 ∧ zbrar[(m + 1) + n0].entry? ∧ zbrar[(m + 1) + n0].key = key

User applied rule constructor cut

And obtained the following new goals

Proof step 39:
zbrar[m + n] = mkzentry(key, adr), n = n1 +1, m + nused0 < # zbrar, m < # zbrar, n ≤ nused0 ⊦ zbrar[m].entry?, key ∈ payload(zbrar, m + 1, nused0), ∃ n0. n0 < nused0 ∧ zbrar[(m + 1) + n0].entry? ∧ zbrar[(m + 1) + n0].key = key

Rule argument

var: n

Additional information

Used simplifier rules: nat freely generated by 0, +1;;% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ 0 ≤ m; (s)% ⊦ mkzentry(key, adr).entry?; (s)