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Proof step 7 from proof valid-idx-update-key (previous step)

kar[m] = key-index(key0, m0), kar[m, key-index(key, m0)][m1] = key-index(key1, m2), m1 < # kar, m1 < n, n ≤ # kar, ∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m2 < # ar ∧ ar[m2].idx = m1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
kar[m, key-index(key, m0)][m1] = key-index(key1, m2), kar[m] = key-index(key0, m0), ar[m2] = elemindex(a, m3), m1 < n, m1 < # kar, n ≤ # kar, ∀ m. m < n → kar[m].idx < # ar ∧ ar[kar[m].idx].idx = m ⊦ m2 < # ar ∧ m3 = m1

Rule argument

spec: elem-index name: elim seq: ⊦ a = ei.elem ∧ m = ei.idx ↔ ei = elemindex(a, m) subst: [ei, a, m] → [ar[m2], a, m3]

Additional information

Used simplifier rules: ⊦ a = ei.elem ∧ m = ei.idx ↔ ei = elemindex(a, m); (elim) Used terms: ar[m2], a, m3