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Proof step 21 from proof keep-range (previous step)

zbr.key = zbrar[m].key, n < nused, m < # zbrar, n < # zbrar, n + 1 < nused, nused ≤ # zbrar, nused ≤ # zbrar[m, zbr] ⊦ n = 0, (ri |> zbrar[m, zbr][n - 1].key) |≤ zbrar[m, zbr][n].key = key-range(zbrar, n, nused, ri)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
zbr.key = zbrar[m].key, n + 1 < nused, n < # zbrar, m < # zbrar, n < nused, n + 1 < # zbrar, nused ≤ # zbrar ⊦ n = 0, (ri |> zbrar[m, zbr][n - 1].key) |≤ zbrar[m, zbr][n].key = (ri |> zbrar[n - 1].key) |≤ zbrar[n].key

Rule argument

Additional information

Used simplifier rules: range-inner: ⊦ n ≠ 0 ∧ n + 1 < nused ∧ nused ≤ # zbrar → key-range(zbrar, n, nused, ri) = (ri |> zbrar[n - 1].key) |≤ zbrar[n].key;%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ # zbrar[n, zbr] = # zbrar; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic