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Proof step 10 from proof modified-stays-reachable (previous step)

path(r ' + [], H) ⊦ ∃ x0. path(r ' + x0, H[(r ' + x0).last, ce]) ∧ (r ' + x0).last = (r ' + []).last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
r ∈ H ⊦ r = null, ∃ x. path(r ' + x, H[(r ' + x).last, ce]) ∧ (r ' + x).last = r

Rule argument

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ r ∈ H ∧ r ≠ null;% ⊦ r '.last = r; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + [] = x0; (s)