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Proof step 14 from proof heap-order-add-smaller (previous step)

kar[m0 + 1] = key-index(key0, m3), kar[m0 / 2] = key-index(key1, m4), kar[m1 / 2] = key-index(key2, m5), m0 < m1, m1 + 1 < # kar, m0 + 1 < # kar, m0 < # kar, key0 < key1, ∀ m. ¬ m1 < m ∧ m ≠ 0 → ¬ kar[m].key < kar[(m - 1) / 2].key ⊦ m0 = m1, key < key2

User applied rule all left

And closed the goal!

Rule argument

pos: left 9 terms: m0 + 1 abort: F discard: F computed: F

Additional information

Used simplifier rules: ⊦ m ≠ n → (m < n + 1 ↔ m < n); (s)% ⊦ m < n → ¬ n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)% ⊦ n ≤ m → m + n0 - n = (m - n) + n0; (s)% ⊦ n + 0 = n; (s)% ⊦ key-index(key, m).key = key; (s) Used terms: m0 + 1