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Proof step 7 from proof eq (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
x0 = a + y0, b ' + y + c ' + z = y0 + c ' + a ' + z0, b ∈ y0 ⊦ x0 = [], a = b, a = c, a ∈ y, a ∈ z, c ∈ z, dups(z)

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] → [x0, a, y0] flags:

Additional information

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