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Proof step 20 from proof keys-shift-left (previous step)

zbrar[n0].key = zbrar[n].key, n0 < n, n0 < # zbrar, nused < # zbrar, n < # zbrar, n0 < nused, n0 + 1 < # zbrar, n ≤ nused, 0 + nused + 1 ≤ # zbrar, ∀ m0, m1. m0 < m1 ∧ m1 < nused + 1 → zbrar[0 + m0].key < zbrar[0 + m1].key ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
zbrar[n0].key = zbrar[n].key, n0 + 1 < # zbrar, n0 < nused, n < # zbrar, n0 < # zbrar, n0 < n, nused < # zbrar, n ≤ nused, ∀ m, m0. m < m0 ∧ ¬ nused < m0 → zbrar[m].key < zbrar[m0].key ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ 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