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Proof step 5 from proof longest-common-prefix (previous step)

x = [], ∀ x. ∃ z, x0, y1. x = z + x0 ∧ y0 = z + y1 ∧ (x0 ≠ [] ∧ y1 ≠ [] → x0.head ≠ y1.head) ⊦ ∃ z, x0, y. x = z + x0 ∧ a ' + y0 = z + y ∧ (x0 ≠ [] ∧ y ≠ [] → x0.head ≠ y.head)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ x. ∃ z, x0, y1. x = z + x0 ∧ y0 = z + y1 ∧ (x0 ≠ [] ∧ y1 ≠ [] → x0.head ≠ y1.head) ⊦ ∃ z, x0, y. [] = z + x0 ∧ a ' + y0 = z + y ∧ (x0 ≠ [] ∧ y ≠ [] → x0.head ≠ y.head)

Proof step 5 from proof longest-common-prefix (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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