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Proof step 180 from proof rem-stays-reachable-aux2 (previous step)

x = r0 + x0, H[r].nxt = H[r1].nxt, r ∈ H, H[r1].nxt ∈ H, path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), path(r1 ' + x + r ', H), r1 ∈ H ⊦ r = null, H[r1].nxt = r1, r1 = r, r1 = H[H[r1].nxt].nxt, H[r1].nxt = H[H[r1].nxt].nxt, r = H[H[r1].nxt].nxt, H[r1].nxt = null, H[H[r1].nxt].nxt ∈ x3, dups(x3), r1 ∈ x3, H[r1].nxt ∈ x3, r ∈ x3, r ∈ x, dups(x), r1 ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 181:
H[r].nxt = H[r1].nxt, path(H[r1].nxt ' + x0 + r ', H), path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), H[r1].nxt ∈ H, r ∈ H, r1 ∈ H ⊦ r1 = null, H[r1].nxt = null, r = H[H[r1].nxt].nxt, H[r1].nxt = H[H[r1].nxt].nxt, r1 = H[H[r1].nxt].nxt, r1 = r, H[r1].nxt = r1, r = null, r1 ∈ x0, dups(x0), H[r1].nxt ∈ x0, r ∈ x0, r ∈ x3, H[r1].nxt ∈ x3, r1 ∈ x3, dups(x3), H[H[r1].nxt].nxt ∈ x3

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));%rec: ⊦ dups(r ' + x0) ↔ ¬ ¬(r ∈ x0 ∨ dups(x0)); from specification list-dup[reflist]%in-06: ⊦ ¬ r ∈ r0 ' + x0 ↔ r ≠ r0 ∧ ¬ r ∈ x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]