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Proof step 11 from proof no-dups-idx-xchg (previous step)

kar[m0] = key-index(key0, m3), kar[m0, kar[m1]][m] = key-index(key, m3), m1 < n, m1 < # kar, m < n, m < # kar, m0 < n, m0 < # kar, ∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx ⊦ m = m1, m = m0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
kar[m0] = key-index(key0, m3), kar[m] = key-index(key, m3), m0 < # kar, m0 < n, m < # kar, m < n, m1 < # kar, m1 < n, ∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx ⊦ m = m0, m = m1

Rule argument

Additional information

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