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Proof step 17 from proof key-range-replace-branches (previous step)

# zbrar0 = # zbrar1, n = m0 + 1, n + 1 < # zbrar1, n < # zbrar1, n < m, n + 1 < m, m ≤ # zbrar1, ∀ n0. n0 ≤ n ∧ n0 ≤ m → zbrar0[n0].key = zbrar1[n0].key ⊦ n + 1 = m, n = 0, (ri |> zbrar0[m0].key) |≤ zbrar0[n].key = (ri |> zbrar1[m0].key) |≤ zbrar1[n].key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# zbrar0 = # zbrar1, m0 + 1 < # zbrar1, 2 + m0 < # zbrar1, m0 + 1 < m, 2 + m0 < m, m ≤ # zbrar1, ∀ n0. n0 ≤ m0 + 1 ∧ n0 ≤ m → zbrar0[n0].key = zbrar1[n0].key ⊦ 2 + m0 = m, (ri |> zbrar0[m0].key) |≤ zbrar0[m0 + 1].key = (ri |> zbrar1[m0].key) |≤ zbrar1[m0 + 1].key

Rule argument

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)