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Proof step 141 from proof rem-stays-reachable-aux2 (previous step)

H[r1].nxt = H[r0].nxt, H[H[r0].nxt].nxt = r0, x = r2 + x0, path(r ' + x2 + r1 ', H), path(r0 ' + x + r1 ', H), path(r ' + (x2 + r1 ') + H[r0].nxt ', H), H[r0].nxt ∈ H, r1 ∈ H, r0 ∈ H ⊦ H[r0].nxt = r1, H[r0].nxt = r0, H[r0].nxt = null, r = r1, r = H[r0].nxt, r0 = r1, r0 = r, r0 = null, r1 = null, dups(x2), dups(x), r1 ∈ x2, r1 ∈ x, r0 ∈ x, r ∈ x2, r0 ∈ x2, H[r0].nxt ∈ x2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 142:
H[r1].nxt = H[r0].nxt, H[H[r0].nxt].nxt = r0, path(H[r0].nxt ' + x0 + r1 ', H), path(r ' + (x2 + r1 ') + H[r0].nxt ', H), path(r ' + x2 + r1 ', H), H[r0].nxt ∈ H, r1 ∈ H, r0 ∈ H ⊦ H[r0].nxt = r1, H[r0].nxt = r0, H[r0].nxt = null, r = r1, r = H[r0].nxt, r0 = r1, r0 = r, r0 = null, r1 = null, dups(x0), dups(x2), H[r0].nxt ∈ x0, r1 ∈ x2, r1 ∈ x0, r0 ∈ x0, r ∈ x2, r0 ∈ x2, H[r0].nxt ∈ x2

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H);% ⊦ dups(r ' + x0) ↔ dups(x0) ∨ r ∈ x0; (ws)% ⊦ r ∈ r0 ' + x0 ↔ ¬(r ≠ r0 ∧ ¬ r ∈ x0); (ss)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)