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Proof step 12 from proof modified-stays-reachable (previous step)

path(r ' + (r0 + x0), H), ∀ r, H, ce. path(r ' + x0, H) → (∃ x1. path(r ' + x1, H[(r ' + x1).last, ce]) ∧ (r ' + x1).last = (r ' + x0).last) ⊦ ∃ 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 13:
path(H[r].nxt ' + x0, H), r ∈ H, ∀ r, H, ce. path(r ' + x0, H) → (∃ x1. path(r ' + x1, H[(r ' + x1).last, ce]) ∧ (r ' + x1).last = (r ' + 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);% ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)