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Proof step 32 from proof no-dups-idx-rec (previous step)

kar[m] = key-index(key1, m3), m < n, n < # kar, m < # kar, m + 1 < # kar, n ≤ # kar, ∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx ⊦ m = n, ∃ m. m < n ∧ key-index(key1, m3) = kar[m]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
kar[m] = key-index(key1, m3), m + 1 < # kar, m < # kar, n < # kar, m < n, ∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx ⊦ m = n, ∃ m. m < n ∧ key-index(key1, m3) = kar[m]

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → m ≤ n; (s)