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Proof step 52 from proof refine-add (previous step)

((del-list(to_delete, n) * ls(rxs, xs)))(H), ((ls(rxs, xs) * del-list(to_delete, n)))(H), n < 2, ls(rxs, xs)(H1), n ≤ # xs, n ≤ 1 ⊦ r = null, (_∃(λ r0. r => a × r0 * ls(r0, xs)))((H1 ++ r)[r, a × rxs]), r ∈ H1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 53:
((ls(rxs, xs) * del-list(to_delete, n)))(H), ((del-list(to_delete, n) * ls(rxs, xs)))(H), n < 2, ls(rxs, xs)(H1), n ≤ 1, n ≤ # xs ⊦ r = null, r ∈ H1, ∃ r0. ((r => a × r0 * ls(r0, xs)))((H1 ++ r)[r, a × rxs])

Rule argument

Additional information

Used simplifier rules: ⊦ (_∃ rP)(H) ↔ (∃ r. rP(r)(H)); (s)