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Proof step 37 from proof keys-shift-left (previous step)

n0 = m + 1, n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), n0 ≤ nused, n ≤ n0, n ≤ nused ⊦ zbrar[n0].key = zbrar[n].key, n0 = 0, ∃ n1. n1 < nused ∧ (n1 < n ⊃ zbrar[n1];zbrar[n1 + 1]).key = zbrar[n0].key, m < nused ∧ (m < n ⊃ zbrar[m];zbrar[m + 1]).key = zbrar[n0].key

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 38:
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

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)%le-one: ⊦ m ≤ n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)