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Proof step 64 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 65:
r0 = H[r0].nxt, path(r ' + (x2 + r1 ') + r0 ', H), path(r0 ' + x1 + r1 ', H), path(r ' + x + r1 ', H), r1 ∈ H, r0 ∈ H ⊦ r = r1, r0 = null, r0 = r, r0 = r1, dups(x2), dups(x), dups(x1), r ∈ x2, r ∈ x, r0 ∈ x1, r0 ∈ x2, r1 ∈ x2, r1 ∈ x, r1 ∈ x1

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)