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Proof step 38 from proof keys-shift-left (previous step)

m + 1 < # zbrar, nused < # zbrar, n < # zbrar, m < nused, m < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused, n ≤ m + 1 ⊦ zbrar[m + 1].key = zbrar[n].key, (m < n ⊃ zbrar[m];zbrar[m + 1]).key = zbrar[m + 1].key, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = zbrar[m + 1].key

User applied rule case distinction

And closed the goal!

Rule argument

pos: right 2

Additional information

Used simplifier rules: ⊦ m < n → (n ≤ m + 1 ↔ n = m + 1); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic