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Proof step 11 from proof modified-stays-reachable (previous step)

∀ r, H, ce. path(r ' + x0, H) ∧ (r ' + x0).last ∈ H → (∃ x1. path(r ' + x1, H[(r ' + x1).last, ce]) ∧ (r ' + x1).last = (r ' + x0).last), path(r ' + (r0 + x0), H), (r ' + (r0 + x0)).last ∈ H ⊦ ∃ x1. path(r ' + x1, H[(r ' + x1).last, ce]) ∧ (r ' + x1).last = (r ' + (r0 + x0)).last

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
(H[r].nxt ' + x0).last ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, ∀ r1, H0, ce0. path(r1 ' + x0, H0) → (∃ x1. path(r1 ' + x1, H0[(r1 ' + x1).last, ce0]) ∧ (r1 ' + x1).last = (r1 ' + x0).last) ⊦ r = null, ∃ x. path(r ' + x, H[(r ' + x).last, ce]) ∧ (r ' + x).last = (H[r].nxt ' + x0).last

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));%path-last: ⊦ path(r ' + x, H) → (¬ (r ' + x).last ∈ H ↔ false);%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]