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Proof step 4 from proof keep-sorted (previous step)

zbr.key = zbrar[n0].key, n0 < # zbrar, ∀ zbr, zbrar, n0, n. zbr.key = zbrar[n0].key ∧ n0 < # zbrar → (sorted(zbrar[n0, zbr], n, m0) ↔ sorted(zbrar, n, m0)) ⊦ sorted(zbrar[n0, zbr], n, m0 +1) ↔ sorted(zbrar, n, m0 +1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
zbr.key = zbrar[n0].key, n0 < # zbrar, ∀ zbr, zbrar, n0, n. zbr.key = zbrar[n0].key ∧ n0 < # zbrar → (sorted(zbrar[n0, zbr], n, m0) ↔ sorted(zbrar, n, m0)) ⊦ sorted(zbrar[n0, zbr], n, m0 + 1) ↔ sorted(zbrar, n, m0 + 1)

Rule argument

Additional information

Used simplifier rules: ⊦ m +1 = m + 1; (s)