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Proof step 12 from proof key-range-replace-branches (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
# 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

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m