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Proof step 9 from proof ll-trav2-next (previous step)

H[r2] = a × r, ((lls(r0, r1, x0) * r1 => a0 × r2 * lls(r2, null, x1) * P))(H) ⊦ r1 = null, r2 = null, ∃ x2, x3, a. x0 + a0 ' + x1 = x2 + a ' + x3 ∧ ((lls(r0, r2, x2) * r2 => a × r * lls(r, null, x3) * P))(H)

User applied rule exists right

And obtained the following new goals

Proof step 10:
H[r2] = a × r, ((lls(r0, r1, x0) * r1 => a0 × r2 * lls(r2, null, x1) * P))(H) ⊦ r1 = null, r2 = null, x0 + a0 ' + x1 = (x0 + a0) + a ' + x1.tail ∧ ((lls(r0, r2, x0 + a0) * r2 => a × r * lls(r, null, x1.tail) * P))(H)

Rule argument

pos: right 3 terms: x0 + a0, x1.tail, a abort: F discard: T computed: F

Additional information

Used terms: x0 + a0, x1.tail, a