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Proof step 2 from proof no-dups-idx-xchg (previous step)

kar[m0] = ki0, kar[m1] = ki1, m0 < n, m1 < n, m0 < # kar, m1 < # kar, no-dups-idx(kar, n) ⊦ no-dups-idx(kar[m0, ki1][m1, ki0], n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
kar[m0, kar[m1]][m1, kar[m0]][m].idx = kar[m0, kar[m1]][m1, kar[m0]][m2].idx, 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

Rule argument

Additional information

Used simplifier rules: no-dups-idx: ⊦ no-dups-idx(kar, n) ↔ (∀ m0, m1. m0 < # kar ∧ m0 < n ∧ m1 < # kar ∧ m1 < n ∧ m0 ≠ m1 → kar[m0].idx ≠ kar[m1].idx);% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # kar[n, ki] = # kar; (s)