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Proof step 9 from proof path-new-irrelevant-strong (previous step)

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

User applied rule constructor cut

And closed the goal!

Rule argument

var: x0

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ r ∈ H ∧ r ≠ null;%path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H);%reflist freely generated by [], +;;% ⊦ r + x0 = r ' + x0; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws)% ⊦ x0 + [] = x0; (s)