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Proof step 9 from proof frommodified (previous step)

x = r0 + x0, path(r ' + x, H[r, ce]), (r ' + x).last ∈ H ⊦ ce.nxt = r, r = (r ' + x).last, r = null, ce.nxt ≠ null ∧ ce.nxt ∈ H ∧ reachable(ce.nxt, (r ' + x).last, H[r, ce])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
path(ce.nxt ' + x0, H[r, ce]), (ce.nxt ' + x0).last ∈ H ⊦ ce.nxt = r, r = (ce.nxt ' + x0).last, r = null, ce.nxt ≠ null ∧ ce.nxt ∈ H ∧ reachable(ce.nxt, (ce.nxt ' + x0).last, H[r, ce])

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H);% ⊦ H[r, ce][r] = ce; (s)% ⊦ r ∈ H[r, ce]; (s)% ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)