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Proof step 47 from proof no-dups-idx-xchg (previous step)

kar[m2] = key-index(key0, m3), kar[m] = key-index(key, m3), kar[m1] = key-index(key1, m4), kar[m0] = key-index(key2, m5), m1 < # kar, m0 < # kar, m1 < n, m0 < n, m < # kar, m < n, m2 < # kar, m2 < n, m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx, ∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx ⊦ m = m1, m = m2, m3 = m5, m3 = m4

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 48:
kar[m2] = key-index(key0, m3), kar[m] = key-index(key, m3), kar[m1] = key-index(key1, m4), kar[m0] = key-index(key2, m5), m1 < # kar, m0 < # kar, m1 < n, m0 < n, m < # kar, m < n, m2 < # kar, m2 < n, m0 ≠ m1 → m5 ≠ m4, ∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx ⊦ m = m1, m = m2, m3 = m5, m3 = m4

Rule argument

Additional information

Used simplifier rules: ⊦ key-index(key, m).idx = m; (s)