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Proof step 7 from proof reachable-split-first (previous step)

path(r ' + x, H), r ∈ H, x.last ∈ H ⊦ H[r].nxt = null, r = null, x = [], r = x.last, 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 ↔ false);%reflist freely generated by [], +;;%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]%e-01: ⊦ r ' + x0 ≠ []; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]