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Proof step 30 from proof valid-idx-move-last (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 31:
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

Rule argument

fma: m2 = m0

Additional information

Used simplifier rules: ⊦ m < # kar → kar[m, ki][m] = ki; (s)% ⊦ key-index(key, m) = key-index(key0, m0) ↔ key = key0 ∧ m = m0; (ws) Used formulas: m2 = m0