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Proof step 13 from proof rem-stays-reachable-aux1 (previous step)

path(H[H[r0].nxt].nxt ' + x1 + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x1, H[r0].nxt ∈ x1, dups(x1), path(H[r0].nxt ' + (H[H[r0].nxt].nxt ' + x1) + H[r0].nxt ', H) ∧ ¬ r0 ∈ H[H[r0].nxt].nxt ' + x1, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
path(H[H[r0].nxt].nxt ' + x1 + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x1, H[r0].nxt ∈ x1, dups(x1), ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x, r0 ≠ H[H[r0].nxt].nxt ∧ ¬ r0 ∈ x1

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));%in-rec: ⊦ r ∈ r0 ' + x0 ↔ ¬ ¬(r = r0 ∨ r ∈ x0); from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]