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Proof step 11 from proof modnotreachable-reachable (previous step)

path(r ' + (r0 + x0), H), ∀ r, H, r1, ce. path(r ' + x0, H) → path(r ' + x0, H[r1, ce]) ∨ reachable(r, r1, H) ⊦ path(r ' + (r0 + x0), H[r1, ce]), reachable(r, r1, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
path(H[r].nxt ' + x0, H), r ∈ H, r ∈ H[r1, ce], ∀ r, H, r1, ce. path(r ' + x0, H) → path(r ' + x0, H[r1, ce]) ∨ reachable(r, r1, H) ⊦ r = null, reachable(r, r1, H), path(H[r1, ce][r].nxt ' + x0, H[r1, ce]) ∧ H[r1, ce][r].nxt = H[r].nxt

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)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)