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Proof step 8 from proof reachable-split-first (previous step)

path(r ' + x, H), r ∈ H, x.last ∈ H ⊦ H[r].nxt = null, r = null, r = x.last, x = [], H[r].nxt ∈ H

User applied rule constructor cut

And closed the goal!

Rule argument

var: x

Additional information

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