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Proof step 23 from proof reach-reachnext (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 24:
(H[r].nxt ' + x2).last = H[(H[r].nxt ' + x1).last].nxt, path(H[r].nxt ' + x2, H), r ∈ H, path(H[r].nxt ' + x1, H), (H[r].nxt ' + x1).last ∈ H, (H[r].nxt ' + x2).last = null ∨ ¬ (H[r].nxt ' + x2).last ∈ 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 = null

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]