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Proof step 17 from proof reach-reachnext (previous step)

(r ' + x0).last = H[(H[r].nxt ' + x1).last].nxt, path(H[r].nxt ' + x1, H), path(r ' + x0, H), r ∈ H, (H[r].nxt ' + x1).last ∈ H, ∀ r, x0, H. (r ' + x0).last = H[(r ' + x1).last].nxt ∧ path(r ' + x0, H) ∧ path(r ' + x1, H) ∧ (r ' + x1).last ∈ H → (r ' + x0).last ≠ null ∧ (r ' + x0).last ∈ H ⊦ r = null, (r ' + x0).last ≠ null ∧ (r ' + x0).last ∈ H

User applied rule constructor cut

And obtained the following new goals

Proof step 18:
(r ' + x0).last = H[(H[r].nxt ' + x1).last].nxt, x0 = r0 + x, path(r ' + x0, H), path(H[r].nxt ' + x1, H), (H[r].nxt ' + x1).last ∈ H, r ∈ H, ∀ r, x0, H. (r ' + x0).last = H[(r ' + x1).last].nxt ∧ path(r ' + x0, H) ∧ path(r ' + x1, H) ∧ (r ' + x1).last ∈ H → (r ' + x0).last ≠ null ∧ (r ' + x0).last ∈ H ⊦ r = null, (r ' + x0).last ≠ null ∧ (r ' + x0).last ∈ H

Rule argument

var: x0

Additional information

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