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Proof step 75 from proof reachable-addnew-rev (previous step)

path(r ' + x, H[r2, ce]), r ∈ H, (r ' + x).last ∈ H ⊦ r2 ∈ x, reachable(r, (r ' + x).last, H), r2 ∈ H, r ∈ x, dups(x), ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, (r ' + x).last, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 76:
r ∈ H, (r ' + x).last ∈ H, path(r ' + x, H) ⊦ r2 ∈ x, reachable(r, (r ' + x).last, H), r2 ∈ H, r ∈ x, dups(x), ∃ r0. reachable(r, r0, H) ∧ H[r0].nxt = r2 ∧ H[r0].nxt ≠ null ∧ reachable(ce.nxt, (r ' + x).last, H)

Rule argument

Additional information

Used simplifier rules: path-new-irrelevant-strong: ⊦ ¬ r2 ∈ H ∧ ¬ r2 ∈ x ∧ r ∈ H → (path(r ' + x, H[r2, ce]) ↔ path(r ' + x, H));%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]