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Proof step 24 from proof ll-trav2-end (previous step)

H[r2] = a × null ⊦ r2 = null, (ll-trav(r0, r1, r2, x) * P)(H) ↔ x ≠ [] ∧ (r1 = null ⊃ (r0 = r2 ∧ (lls(r2, null, x) * P)(H)); (∃ y, b. x = y + b ' + a ' ∧ (lls(r0, r1, y) * r1 => b × r2 * r2 => a × null * P)(H)))

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 16:
(ll-trav(r0, r1, r2, x) * P)(H), H[r2] = a × null ⊦ x ≠ [] ∧ (r1 = null ⊃ (r0 = r2 ∧ (lls(r2, null, x) * P)(H)); (∃ y, b. x = y + b ' + a ' ∧ (lls(r0, r1, y) * r1 => b × r2 * r2 => a × null * P)(H))), r2 = null

Rule argument

[CASEDARG : pos: right 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]