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Proof step 8 from proof sorted-shift-left (previous step)

m0 + 1 < # zbrar, 2 + m0 < # zbrar, m0 < nused, nused < # zbrar, n < # zbrar, m < nused, m0 < m, m + 1 < # zbrar, m < # zbrar, m0 + 1 < nused, m0 < # zbrar, m0 < n, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ zbrar[m0].key < (m < n ⊃ zbrar[m];zbrar[m + 1]).key

User applied rule case distinction

And obtained the following new goals

Proof step 9:
m0 < n, m0 < # zbrar, m0 + 1 < nused, m < # zbrar, m + 1 < # zbrar, m0 < m, m < nused, n < # zbrar, nused < # zbrar, m0 < nused, 2 + m0 < # zbrar, m0 + 1 < # zbrar, m < n, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ zbrar[m0].key < zbrar[m].key
Proof step 12:
m0 < n, m0 < # zbrar, m0 + 1 < nused, m < # zbrar, m + 1 < # zbrar, m0 < m, m < nused, n < # zbrar, nused < # zbrar, m0 < nused, 2 + m0 < # zbrar, m0 + 1 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ zbrar[m0].key < zbrar[m + 1].key, m < n

Rule argument

pos: right 1

Proof step 8 from proof sorted-shift-left (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information