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Proof step 31 from proof valid-idx-move-last (previous step)

ar[m3] = elemindex(a, m4), kar[m] = key-index(key, m1), kar[m0, key-index(key, m1)][m2] = key-index(key0, m3), m2 + 1 < # kar, m < # kar, m2 < m, m2 < # kar, ∀ m2. ¬ m < m2 → kar[m2].idx < # ar ∧ ar[kar[m2].idx].idx = m2 ⊦ m2 = m0, m3 = m1, m3 < # ar ∧ m4 = m2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
kar[m] = key-index(key, m1), ar[m3] = elemindex(a, m4), kar[m2] = key-index(key0, m3), m2 < # kar, m2 < m, m < # kar, m2 + 1 < # kar, ∀ m2. ¬ m < m2 → kar[m2].idx < # ar ∧ ar[kar[m2].idx].idx = m2 ⊦ m2 = m0, m3 = m1, m3 < # ar ∧ m4 = m2

Rule argument

Additional information

Used simplifier rules: ⊦ m ≠ n → kar[n, ki][m] = kar[m]; (s)