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Proof step 3 from proof ll-trav2-next (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 4:
H[r2] = a × r, r1 = null, ((ll-trav(r0, r1, r2, x) * P))(H) ⊦ r2 = null, ∃ x0, x1, a0. x = x0 + a0 ' + x1 ∧ ((lls(r0, r2, x0) * r2 => a0 × r * lls(r, null, x1) * P))(H)
Proof step 8:
H[r2] = a × r, ((ll-trav(r0, r1, r2, x) * P))(H) ⊦ r1 = null, r2 = null, ∃ x0, x1, a0. x = x0 + a0 ' + x1 ∧ ((lls(r0, r2, x0) * r2 => a0 × r * lls(r, null, x1) * P))(H)

Rule argument

fma: r1 = null

Additional information

Used formulas: r1 = null