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Proof step 130 from proof rem-stays-reachable-aux2 (previous step)

¬ x1 ≠ [], H[H[r0].nxt].nxt = r0, path(r ' + x1 + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x + (r ' + x1).last ', H), (r ' + x1).last ∈ H, path(r ' + x1, H) ⊦ H[r0].nxt = null, r0 = r, r = H[r0].nxt, H[r0].nxt = r0, r0 = null, r0 = (r ' + x1).last, r ∈ x1, H[r0].nxt ∈ x1, r0 ∈ x1, dups(x1), r0 ∈ x, (r ' + x1).last ∈ x, dups(x)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 131:
H[H[r0].nxt].nxt = r0, H[r].nxt = H[r0].nxt, H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x + r ', H), r ∈ H ⊦ H[r0].nxt = null, r0 = r, r = H[r0].nxt, H[r0].nxt = r0, r0 = null, r = null, dups(x), r0 ∈ x, r ∈ x

Rule argument

Additional information

Used simplifier rules: path-two: ⊦ path(r ' + r0 ', H) ↔ ¬ ¬(r ∈ H ∧ r0 ∈ H ∧ r ≠ null ∧ r0 ≠ null ∧ H[r].nxt = r0);%path-one: ⊦ path(r ', H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null);%e-01: ⊦ ¬ dups([]); from specification list-dup[reflist]%in-empty: ⊦ ¬ r ∈ []; from specification list[reflist]%Nil: ⊦ [] + x0 = x0; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]