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Proof step 24 from proof valid-idx-move-last (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 25:
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 = m0, m2 + 1 < # kar, m < # kar, m2 < m, m2 < # kar, # ar ≤ m1, ∀ m2. ¬ m < m2 → kar[m2].idx < # ar ∧ ar[kar[m2].idx].idx = m2 ⊦
Proof step 27:
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

Rule argument

fma: m2 = m0

Additional information

Used formulas: m2 = m0