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Proof step 5 from proof ll-trav2-next (previous step)

H[r0] = a × r, ((lls(r0, null, x) * P))(H) ⊦ r0 = null, ∃ x0, x1, a0. x = x0 + a0 ' + x1 ∧ ((lls(r0, r0, x0) * r0 => a0 × r * lls(r, null, x1) * P))(H)

User applied rule exists right

And obtained the following new goals

Proof step 6:
H[r0] = a × r, ((lls(r0, null, x) * P))(H) ⊦ r0 = null, x = [] + x.head ' + x.tail ∧ ((lls(r0, r0, []) * r0 => x.head × r * lls(r, null, x.tail) * P))(H)

Rule argument

pos: right 2 terms: [], x.tail, x.head abort: F discard: T computed: F

Additional information

Used terms: [], x.tail, x.head