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

H[r1] = a × r, ((lls(r0, r1, x0) * lls(r1, null, x1) * P))(H) ⊦ r1 = null, x0 + x1 = (x0 + x1.head) + x1.tail ∧ ((lls(r0, r, x0 + x1.head) * lls(r, null, x1.tail) * P))(H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ⊦ x + y = x + z ↔ y = z; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ x + a = x + a '; (s)