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Proof step 6 from proof reachable-split-first (previous step)

(r ' + x).last ∈ H, path(r ' + x, H), r ∈ H ⊦ x = [], r = (r ' + x).last, H[r].nxt = null, r = null, H[r].nxt ∈ H

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
path(r ' + x, H), r ∈ H, x.last ∈ H ⊦ H[r].nxt = null, r = null, x = [], r = x.last, H[r].nxt ∈ H

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l-02: ⊦ x0 ≠ [] → (r ' + x0).last = x0.last; from specification list-last[reflist]