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Proof step 22 from proof reach-reachnext (previous step)

(r ' + x0).last = H[(H[r].nxt ' + x1).last].nxt, (H[r].nxt ' + x1).last ∈ H, path(H[r].nxt ' + x1, H), r ∈ H, path(r ' + x0, H), ∀ r1, x, H0. (r1 ' + x).last ≠ H0[(r1 ' + x1).last].nxt ∨ ¬ path(r1 ' + x, H0) ∨ ¬ path(r1 ' + x1, H0) ∨ ¬ (r1 ' + x1).last ∈ H0 ∨ (r1 ' + x).last ≠ null ∧ (r1 ' + x).last ∈ H0, (r ' + x0).last = null ∨ ¬ (r ' + x0).last ∈ H ⊦ r = null

User applied rule constructor cut

And obtained the following new goals

Proof step 23:
x0 = r0 + x2, (r ' + x0).last = H[(H[r].nxt ' + x1).last].nxt, (H[r].nxt ' + x1).last ∈ H, path(H[r].nxt ' + x1, H), r ∈ H, path(r ' + x0, H), ∀ r1, x, H0. (r1 ' + x).last ≠ H0[(r1 ' + x1).last].nxt ∨ ¬ path(r1 ' + x, H0) ∨ ¬ path(r1 ' + x1, H0) ∨ ¬ (r1 ' + x1).last ∈ H0 ∨ (r1 ' + x).last ≠ null ∧ (r1 ' + x).last ∈ H0, (r ' + x0).last = null ∨ ¬ (r ' + x0).last ∈ H ⊦ r = null

Rule argument

var: 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]