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Proof step 18 from proof reach-reachnext (previous step)

(r ' + x0).last = H[r].nxt, path(r ' + x0, H), r ∈ H, H[r].nxt = null ∨ ¬ H[r].nxt ∈ H ⊦ r = null

User applied rule structural induction

And obtained the following new goals

Proof step 19:
∀ r, H. (r ' + x).last = H[r].nxt ∧ path(r ' + x, H) ∧ r ∈ H ∧ (H[r].nxt = null ∨ ¬ H[r].nxt ∈ H) → r = null, (r ' + (r0 + x)).last = H[r].nxt, path(r ' + (r0 + x), H), r ∈ H, H[r].nxt = null ∨ ¬ H[r].nxt ∈ H ⊦ r = null

Rule argument

indvar: x0

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%reflist freely generated by [], +;;%app: ⊦ x0 + [] = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]