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Proof step 140 from proof rem-stays-reachable-aux2 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 141:
H[r1].nxt = H[r0].nxt, H[H[r0].nxt].nxt = r0, path(H[r0].nxt ' + x0 + r1 ', H), r0 ∈ H, H[r0].nxt ∈ H, path(r ' + (x2 + r1 ') + H[r0].nxt ', H), path(r ' + x2 + r1 ', H), r1 ∈ H ⊦ r1 = null, H[r0].nxt = r1, r = r1, r0 = r1, r0 = null, H[r0].nxt = r0, r = H[r0].nxt, r0 = r, H[r0].nxt = null, dups(x0), H[r0].nxt ∈ x0, r1 ∈ x0, r0 ∈ x0, dups(x2), r1 ∈ x2, r0 ∈ x2, H[r0].nxt ∈ x2, r ∈ 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));%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]