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Proof step 54 from proof rem-stays-reachable-aux2 (previous step)

(r ' + x1).last = r1, (r0 ' + x0).last = r1, r0 = H[r0].nxt, x = x2 + r1 ', path(r ' + x1, H), path(r0 ' + x0, H), path(r ' + x + r0 ', H), r0 ∈ H, r1 ∈ H ⊦ r0 = r, r0 = null, x = [], dups(x0), dups(x1), dups(x), r0 ∈ x, r0 ∈ x0, r ∈ x1, r ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 55:
(r ' + x1).last = (r0 ' + x0).last, r0 = H[r0].nxt, path(r ' + (x2 + (r0 ' + x0).last ') + r0 ', H), path(r0 ' + x0, H), path(r ' + x1, H), (r0 ' + x0).last ∈ H, r0 ∈ H ⊦ r = (r0 ' + x0).last, r0 = null, r0 = r, r0 = (r0 ' + x0).last, dups(x1), dups(x0), dups(x2), r ∈ x2, r ∈ x1, r0 ∈ x0, r0 ∈ x2, (r0 ' + x0).last ∈ x2

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)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + r ' ≠ []; (s)