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Proof step 36 from proof no-dups-idx-xchg (previous step)

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

Heuristic quantifier applied rule all left

And obtained the following new goals

Proof step 37:
kar[m] = key-index(key, m3), kar[m2] = key-index(key0, m3), m2 < n, m2 < # kar, m < n, m < # kar, m0 < n, m1 < n, m0 < # kar, m1 < # kar, m2 < # kar ∧ m2 < n ∧ m1 < # kar ∧ m1 < n ∧ m2 ≠ m1 → kar[m2].idx ≠ kar[m1].idx, ∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx ⊦ m = m2, m = m1, m = m0, m2 = m1, m2 = m0

Rule argument

pos: left 11 terms: m2, m1

Additional information

Used terms: m2, m1