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Proof step 13 from proof key-range-replace-branches (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
# zbrar0 = # zbrar1, m + 1 < # zbrar1, ∀ n. n ≤ m + 1 ∧ n ≤ 2 + m → zbrar0[n].key = zbrar1[n].key ⊦ ri |> zbrar0[m].key = ri |> zbrar1[m].key

Rule argument

Additional information

Used simplifier rules: 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)