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Proof step 7 from proof firstn-last-rec (previous step)

m < # y, ∀ x0. m < # x0 → x0.first ' + firstn(m, x0.rest) = firstn(m, x0) + x0[m] ' ⊦ y.first ' + firstn(m, y.rest) = firstn(m, y) + y[m] ', y = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
y = a + y0, m < # y, ∀ x0. m < # x0 → x0.first ' + firstn(m, x0.rest) = firstn(m, x0) + x0[m] ' ⊦ a ' + firstn(m, y0) = firstn(m, y) + y[m] ', y = []

Rule argument

spec: list-data inst: name: elim-list-c seq: x ≠ [] ⊦ a = x.first ∧ y = x.rest ↔ x = a + y subst: [x, a, y] → [y, a, y0] flags:

Additional information

Used simplifier rules: x ≠ [] ⊦ a = x.first ∧ y = x.rest ↔ x = a + y; (elim) Used terms: y, a, y0