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Proof step 4 from proof payload-mod (previous step)

n < nused0 +1, sorted(zbrar, m, nused0 +1), m + nused0 +1 ≤ # zbrar, ∀ n, zbrar, m, adr. n < nused0 ∧ sorted(zbrar, m, nused0) ∧ m + nused0 ≤ # zbrar → payload(zbrar[m + n, mkzentry(zbrar[m + n].key, adr)], m, nused0) = payload(zbrar, m, nused0)[zbrar[m + n].key, adr] ⊦ payload(zbrar[m + n, mkzentry(zbrar[m + n].key, adr)], m, nused0 +1) = payload(zbrar, m, nused0 +1)[zbrar[m + n].key, adr]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
m + nused0 < # zbrar, sorted(zbrar, m, nused0 + 1), n ≤ nused0, ∀ n, zbrar, m, adr. n < nused0 ∧ sorted(zbrar, m, nused0) ∧ m + nused0 ≤ # zbrar → payload(zbrar[m + n, mkzentry(zbrar[m + n].key, adr)], m, nused0) = payload(zbrar, m, nused0)[zbrar[m + n].key, adr] ⊦ payload(zbrar[m + n, mkzentry(zbrar[m + n].key, adr)], m, nused0 + 1) = payload(zbrar, m, nused0 + 1)[zbrar[m + n].key, adr]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n + 1 ↔ ¬ n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m +1 = m + 1; (s)