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Proof step 137 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 138:
H[H[r0].nxt].nxt = r0, path(r ' + (x2 + r1 ') + H[r0].nxt ', H), path(r0 ' + x + r1 ', H), path(r ' + x2 + r1 ', H), r0 ∈ H, r1 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = r0, H[r0].nxt = r1, r = H[r0].nxt, r = r1, r0 = null, r0 = r, r0 = r1, dups(x), dups(x2), H[r0].nxt ∈ x2, r0 ∈ x2, r ∈ x2, r0 ∈ x, r1 ∈ x, r1 ∈ 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)