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Proof step 20 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
path(r ' + x + H[r0].nxt ', H), reachable(r, r0, H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = null, r0 = r, r0 ∈ x, reachable(r, (r ' + x).last, H) ∧ ¬ reachable(r0, (r ' + x).last, H)

Rule argument

Additional information

Used simplifier rules: path-last-nxt: ⊦ path(r ' + x + r0 ', H) → (H[(r ' + x).last].nxt ≠ r0 ↔ false);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]