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Proof step 18 from proof key-range-replace-branches (previous step)

# 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

User applied rule all left

And obtained the following new goals

Proof step 19:
# zbrar0 = # zbrar1, 2 + m0 < m, m0 + 1 < m, 2 + m0 < # zbrar1, m0 + 1 < # zbrar1, m ≤ # zbrar1, m0 ≤ m0 + 1 ∧ m0 ≤ m → zbrar0[m0].key = zbrar1[m0].key, ∀ 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

pos: left 7 terms: m0 abort: F discard: F computed: T

Additional information

Used terms: m0