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Proof step 4 from proof ll-trav1-end (previous step)

H[r1] = a × null, ∃ x0, x1. x = x0 + x1 ∧ ((lls(r0, r1, x0) * lls(r1, null, x1) * P))(H) ⊦ r1 = null, x ≠ [] ∧ (∃ y. x = y + a ' ∧ ((lls(r0, r1, y) * r1 => a × null * P))(H))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
H[r1] = a × null, ((lls(r0, r1, x1) * lls(r1, null, x0) * P))(H) ⊦ r1 = null, x1 + x0 ≠ [] ∧ (∃ y. x1 + x0 = y + a ' ∧ ((lls(r0, r1, y) * r1 => a × null * P))(H))

Proof step 4 from proof ll-trav1-end (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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