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Proof step 41 from proof rem-stays-reachable-aux2 (previous step)

¬ x ≠ [], r0 = H[r0].nxt, (r ' + x1).last = (r ' + x).last, (r0 ' + x0).last = (r ' + x).last, (r ' + x).last ∈ H, path(r0 ' + x0, H), r0 ∈ H, path(r ' + x + r0 ', H), path(r ' + x1, H) ⊦ r0 = r, r0 = null, dups(x), r ∈ x, dups(x1), r ∈ x1, dups(x0), r0 ∈ x0, r0 ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
(H[r].nxt ' + x0).last = r, (r ' + x1).last = r, H[r].nxt = H[H[r].nxt].nxt, H[r].nxt ∈ H, path(H[r].nxt ' + x0, H), r ∈ H, path(r ' + x1, H) ⊦ r = null, H[r].nxt = null, H[r].nxt = r, H[r].nxt ∈ x0, dups(x0), r ∈ x1, dups(x1)

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);%in-empty: ⊦ ¬ r ∈ []; from specification list[reflist]%e-01: ⊦ ¬ dups([]); from specification list-dup[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]