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Proof step 6 from proof firstn-last-rec (previous step)

m + 1 < # x, ∀ x0. m < # x0 → x0.head ' + firstn(m, x0.tail) = firstn(m, x0) + x0[m] ' ⊦ x.tail.head ' + firstn(m, x.tail.tail) = firstn(m, x.tail) + x.tail[m] ', x = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
x = a + y, m + 1 < # x, ∀ x0. m < # x0 → x0.head ' + firstn(m, x0.tail) = firstn(m, x0) + x0[m] ' ⊦ y.head ' + firstn(m, y.tail) = firstn(m, y) + y[m] ', x = []

Rule argument

spec: list-data name: elim-list-c seq: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y subst: [x, a, y] → [x, a, y]

Additional information

Used simplifier rules: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y; (elim) Used terms: x, a, y