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Proof step 5 from proof heap-order-pull-down-parent (previous step)

m1 + 1 < n, kar[m1 + 1, kar[m1 / 2]][m0].key < kar[m1 + 1, kar[m1 / 2]][(m0 - 1) / 2].key, m0 < n, m0 < # kar, m1 + 1 < # kar, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ m0 = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
m0 = m2 + 1, m1 + 1 < # kar, m0 < # kar, m0 < n, kar[m1 + 1, kar[m1 / 2]][m0].key < kar[m1 + 1, kar[m1 / 2]][m2 / 2].key, m1 + 1 < n, n ≤ # kar, ∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ m0 = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m0, m2]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m0, m2