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Proof step 8 from proof blast-head (previous step)

a0 ' + y = y0 + a1 ', a ∈ y0, a = a0 ∨ a ∈ y, a0 ∈ y0 ∨ a0 = a1, a1 = a0 ∨ a1 ∈ y ⊦ y0.head = a0

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: list-data name: elim-list-c seq: x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y subst: [x, a, y] → [y0, a2, y1]

Additional information

Used simplifier rules: ⊦ a + x = a ' + x; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ' + x = b ' + y ↔ a = b ∧ x = y; (ws)% ⊦ [] + x = x; (s)% ⊦ a ' = b ' + x ↔ a = b ∧ x = []; (ws)% ⊦ ¬ a ∈ []; (s)%x ≠ [] ⊦ a = x.head ∧ y = x.tail ↔ x = a + y; (elim) Used terms: y0, a2, y1