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Proof step 13 from proof reachable-addnew (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
path(H[r].nxt ' + x0, H), r ∈ H, r ∈ H[r2, ce], ∀ r, H, r2, ce. path(r ' + x0, H) → x0 = [] ∨ path(r ' + x0, H[r2, ce]) ∨ r2 ∈ H ⊦ r = null, path(H[r].nxt ' + x0, H[r2, ce]), 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 ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws)% ⊦ r ∈ H ∧ ¬ r0 ∈ H → H[r0, ce][r] = H[r]; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r ' + x0 ≠ []; (s)% ⊦ r + x0 = r ' + x0; (s)