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Proof step 39 from proof rem-stays-reachable-aux2 (previous step)

(r0 ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, x2 = x + H[r0].nxt ', x2 = x3 + r0 ', path(r ' + x2, H), path(r0 ' + x0, H), path(r ' + x1, H), H[r0].nxt ∈ x2, (r ' + x).last ∈ H, r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = null, r0 = r, x2 = [], dups(x2), dups(x1), dups(x0), r ∈ x2, r ∈ x1, r0 ∈ x0, r0 ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
(r0 ' + x0).last = (r ' + x).last, (r ' + x1).last = (r ' + x).last, r0 = H[r0].nxt, path(r ' + x + r0 ', H), path(r0 ' + x0, H), path(r ' + x1, H), (r ' + x).last ∈ H, r0 ∈ H ⊦ r0 = null, r0 = r, dups(x), dups(x1), dups(x0), r ∈ x, r ∈ x1, r0 ∈ x0, r0 ∈ x

Rule argument

Additional information

Used simplifier rules: ⊦ dups(x0 + r ') ↔ r ∈ x0 ∨ dups(x0); (ws)% ⊦ r ∈ r0 ' ↔ r = r0; (s)% ⊦ r ∈ x0 + x1 ↔ r ∈ x0 ∨ r ∈ x1; (s)% ⊦ x0 + r ' ≠ []; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + r ' = x1 + r0 ' ↔ x0 = x1 ∧ r = r0; (ws)