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Proof step 13 from proof reachable-addnew-rev (previous step)

path(r ' + x, H[(r ' + x).last, ce]), r ∈ H ⊦ x = [], dups(x), r ∈ x, (r ' + x).last ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = (r ' + x).last ∧ H[r0].nxt ≠ null

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
path(r ' + x, H[x.last, ce]), r ∈ H ⊦ x = [], dups(x), r ∈ x, x.last ∈ H, ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = x.last ∧ H[r0].nxt ≠ null

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)