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Proof step 4 from proof path-new-irrelevant-strong (previous step)

r ∈ H, ∀ r, H, r2, ce. r ∈ H → (path(r ' + x0, H[r2, ce]) ↔ path(r ' + x0, H)) ∨ r2 ∈ H ∨ r2 ∈ x0 ⊦ path(r ' + (r0 + x0), H[r2, ce]) ↔ path(r ' + (r0 + x0), H), r2 ∈ r0 + x0, r2 ∈ H

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
r ∈ H, ∀ r, H, r2, ce. r ∈ H → (path(r ' + x0, H[r2, ce]) ↔ path(r ' + x0, H)) ∨ r2 ∈ H ∨ r2 ∈ x0 ⊦ r ∈ H[r2, ce] ∧ path(H[r].nxt ' + x0, H[r2, ce]) ↔ path(H[r].nxt ' + x0, H), r = null, r2 = H[r].nxt, r2 ∈ x0, r2 ∈ H

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);% ⊦ r ∈ r0 ' + x0 ↔ ¬(r ≠ r0 ∧ ¬ r ∈ x0); (ss)% ⊦ r ∈ H ∧ ¬ r0 ∈ H → H[r0, ce][r] = H[r]; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)