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Proof step 11 from proof reachable-addnewtonull-rev (previous step)

ce.nxt = null, path(r ' + (r0 + x0), H[r2, ce]), (r ' + (r0 + x0)).last ∈ H, ∀ ce, r, H, r2. ce.nxt = null ∧ path(r ' + x0, H[r2, ce]) ∧ (r ' + x0).last ∈ H → path(r ' + x0, H) ∨ r2 ∈ H ⊦ path(r ' + (r0 + x0), H), r2 ∈ H

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
ce.nxt = null, path(H[r2, ce][r].nxt ' + x0, H[r2, ce]), r ∈ H[r2, ce], (H[r2, ce][r].nxt ' + x0).last ∈ H, ∀ ce, r, H, r2. ce.nxt = null ∧ path(r ' + x0, H[r2, ce]) ∧ (r ' + x0).last ∈ H → path(r ' + x0, H) ∨ r2 ∈ H ⊦ r = null, r2 ∈ H, r ∈ H ∧ path(H[r].nxt ' + x0, 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 ∈ H ∧ ¬ r0 ∈ H → H[r0, ce][r] = H[r]; (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)