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Proof step 2 from proof heap-order-remove-last (previous step)

n < # kar, heap-order(kar, n + 1) ⊦ heap-order(kar, n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
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

Rule argument

Additional information

Used simplifier rules: heap-order: ⊦ heap-order(kar, n) ↔ (∀ m. m < n ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key);% ⊦ m +1 = m + 1; (s)% ⊦ m < n → n ≠ 0; (s)%trans: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m < n + 1 ↔ ¬ n < m; (s)