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Proof step 3 from proof heap-order-add-smaller (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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

Rule argument

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

Additional information

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