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Proof step 6 from proof keep-sorted (previous step)

zbr.key = zbrar[n0].key, m0 = m +1, 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 7:
zbr.key = zbrar[n0].key, n0 < # zbrar, ∀ zbr0, zbrar0, n1, n2. zbr0.key = zbrar0[n1].key ∧ n1 < # zbrar0 → (sorted(zbrar0[n1, zbr0], n2, m + 1) ↔ sorted(zbrar0, n2, m + 1)) ⊦ sorted(zbrar[n0, zbr], n, 2 + m) ↔ sorted(zbrar, n, 2 + m)

Rule argument

Additional information

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