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Proof step 7 from proof less-same (previous step)

∀ n0, a1. n0 + 1 < # x0 → less#(a1, x0[n0, x0[n0 + 1]][n0 + 1, x0[n0]]) = less#(a1, x0) ⊦ less#(a, (x0.head ' + x0)[1, a0]) = (a0 < a ⊃ 1;0) + less#(a, x0), x0 = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
x0 = a2 + y, ∀ n0, a1. n0 + 1 < # x0 → less#(a1, x0[n0, x0[n0 + 1]][n0 + 1, x0[n0]]) = less#(a1, x0) ⊦ less#(a, (a2 ' + x0)[1, a0]) = (a0 < a ⊃ 1;0) + less#(a, x0), x0 = []

Rule argument

spec: list-data name: elim-list-c seq: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y subst: [x, a, y] → [x0, a2, y]

Additional information

Used simplifier rules: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y; (elim) Used terms: x0, a2, y