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Proof step 7 from proof ll-trav1-next (previous step)

(((r1 => a0 × r * lls(r, null, y)) * lls(r0, r1, x0) * P))(H) ⊦ r1 = null, ((lls(r0, r, x0 + a0 ') * lls(r, null, y) * P))(H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ lls(r0, r2, x + a ') = _∃(λ r1. lls(r0, r1, x) * r1 => a × r2)
Proof step 9:
(((r1 => a0 × r * lls(r, null, y)) * lls(r0, r1, x0) * P))(H) ⊦ r1 = null, ((_∃(λ r1. lls(r0, r1, x0) * r1 => a0 × r) * lls(r, null, y) * P))(H)

Rule argument

spec: <toplevel> name: lls-unfold-tail seq: ⊦ lls(r0, r2, x + a ') = _∃(λ r1. lls(r0, r1, x) * r1 => a × r2) subst: [a, x, r2, r0] → [a0, x0, r, r0] flags: <all paths>

Additional information

Used terms: a0, x0, r, r0