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

m3 / 2 = m1 + 1, kar[m3 + 1] = key-index(key0, m0), kar[m1 / 2] = key-index(key, m), kar[m1 + 1, key-index(key, m)][m3 / 2] = key-index(key1, m4), m3 + 1 < # kar, key0 < key1, m1 + 1 < # kar, m3 < m1, ∀ m2. ¬ m1 < m2 ∧ m2 ≠ 0 → ¬ kar[m2].key < kar[(m2 - 1) / 2].key ⊦ m3 = m1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
m3 / 2 = m1 + 1, kar[m1 / 2] = key-index(key1, m), kar[m3 + 1] = key-index(key0, m0), m3 < m1, key0 < key1, m3 + 1 < # kar, m1 + 1 < # kar, ∀ m2. ¬ m1 < m2 ∧ m2 ≠ 0 → ¬ kar[m2].key < kar[(m2 - 1) / 2].key ⊦ m3 = m1

Rule argument

Additional information

Used simplifier rules: ⊦ key-index(key, m) = key-index(key0, m0) ↔ key = key0 ∧ m = m0; (ws)% ⊦ m < # kar → kar[m, ki][m] = ki; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic