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Proof step 27 from proof valid-idx-move-last (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
kar[m] = key-index(key, m1), ar[m1, ar[m1].idx:= m0][m1] = elemindex(a, m4), kar[m2] = key-index(key0, m1), m2 < # kar, m2 < m, m < # kar, m2 + 1 < # kar, # ar ≤ m1, ∀ m2. ¬ m < m2 → kar[m2].idx < # ar ∧ ar[kar[m2].idx].idx = m2 ⊦ m2 = m0

Rule argument

Additional information

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