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Proof step 18 from proof no-dups-idx-xchg (previous step)

kar[m0, kar[m1]][m2] = key-index(key0, m3), kar[m0, kar[m1]][m1, kar[m0]][m] = key-index(key, m3), m = m1, m2 < n, m2 < # kar, m < n, m < # kar, m0 < n, m1 < n, m0 < # kar, m1 < # kar, ∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx ⊦ m = m2, m2 = m1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
kar[m0, kar[m1]][m2] = key-index(key0, m3), kar[m0] = key-index(key, m3), m0 < # kar, m0 < n, m1 < # kar, m1 < n, m2 < # kar, m2 < n, ∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx ⊦ m1 = m2

Rule argument

Additional information

Used simplifier rules: m < # kar ⊦ kar[m, ki][m] = ki; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ # kar[n, ki] = # kar; (s)