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Proof step 133 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 134:
H[r].nxt = H[r0].nxt, H[H[r0].nxt].nxt = r0, path(H[r0].nxt ' + x0 + r ', H), H[r0].nxt ∈ H, r ∈ H, r0 ∈ H ⊦ H[r0].nxt = r0, H[r0].nxt = null, r = null, r = H[r0].nxt, r0 = r, r0 = null, dups(x0), H[r0].nxt ∈ x0, r ∈ x0, r0 ∈ x0

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)