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Proof step 25 from proof frommodified (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
path(ce.nxt ' + x, H[r, ce]), ce.nxt ∈ H, x.last ∈ H ⊦ ce.nxt = null, r = null, r = x.last, x = [], reachable(r, x.last, H[r, ce])

Rule argument

Additional information

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