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Proof step 128 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 129:
H[H[r0].nxt].nxt = r0, path(r ' + x1 + H[r0].nxt ', H), path(r0 ' + x + (r ' + x1).last ', H), path(r ' + x1, H), r0 ∈ H, (r ' + x1).last ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = null, H[r0].nxt = r0, r = H[r0].nxt, r0 = null, r0 = r, r0 = (r ' + x1).last, dups(x1), dups(x), H[r0].nxt ∈ x1, r0 ∈ x1, r ∈ x1, r0 ∈ x, (r ' + x1).last ∈ 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)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + r ' ≠ []; (s)