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Proof step 1 from proof key-range-replace-branches (conclusion)

⊦ n < m ∧ m ≤ # zbrar0 ∧ # zbrar0 = # zbrar1 ∧ (∀ n0. n0 ≤ n ∧ n0 ≤ m → zbrar0[n0].key = zbrar1[n0].key) → key-range(zbrar0, n, m, ri) = key-range(zbrar1, n, m, ri)

System applied rule normalize

And obtained the following new goals

Proof step 2:
# zbrar0 = # zbrar1, n < m, m ≤ # zbrar0, ∀ n0. n0 ≤ n ∧ n0 ≤ m → zbrar0[n0].key = zbrar1[n0].key ⊦ key-range(zbrar0, n, m, ri) = key-range(zbrar1, n, m, ri)

Proof step 1 from proof key-range-replace-branches (conclusion)

System applied rule normalize

And obtained the following new goals

Rule argument

Additional information