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Proof step 3 from proof heap-order-remove-last (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
m = m0 + 1, m + 1 < # kar, n < # kar, kar[m].key < kar[m0 / 2].key, m < n, m < # kar, ∀ m. ¬ n < m ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ m = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m, m1]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m, m1