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Proof step 15 from proof keep-range (previous step)

zbr.key = zbrar[m].key, n < nused, m < # zbrar, n < # zbrar, nused ≤ # zbrar ⊦ key-range(zbrar[m, zbr], n, nused, ri) = key-range(zbrar, n, nused, ri), n + 1 < nused

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
zbr.key = zbrar[m].key, m < # zbrar, n < # zbrar ⊦ key-range(zbrar[m, zbr], n, n + 1, ri) = key-range(zbrar, n, n + 1, ri)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%eqle-one: ⊦ m = n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n → (n ≤ m + 1 ↔ n = m + 1); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)