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Proof step 6 from proof reachnext (previous step)

(r0 ' + x).last = H[r0].nxt, path(r0 ' + x, H) ⊦ r0 = null, H[r0].nxt ≠ null ∧ H[r0].nxt ∈ H

User applied rule constructor cut

And closed the goal!

Rule argument

var: x

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));%path-first-in-H: ⊦ path(r ' + x, H) → (¬ r ∈ H ↔ false);%null-not-start-of-path: ⊦ ¬ path(null ' + x, H);%reflist freely generated by [], +;;%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]