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Proof step 8 from proof eq (previous step)

b ' + y + c ' + z = x0.tail + c ' + x0.head ' + z0, b ∈ x0.tail ⊦ x0.head = b, x0.head = c, x0 = [], dups(z), x0.head ∈ y, x0.head ∈ z, c ∈ z

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
b ' + y + c ' + z = y0 + c ' + a ' + z0, x0 = a + y0, b ∈ y0 ⊦ a = c, a = b, x0 = [], dups(z), c ∈ z, a ∈ z, a ∈ y

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, a, y0]

Additional information

Used simplifier rules: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y; (elim) Used terms: x0, a, y0