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Proof step 181 from proof rem-stays-reachable-aux2 (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 182:
x0 = r0 + x, 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

var: x0

Additional information

Used simplifier rules: path-two: ⊦ path(r ' + r0 ', H) ↔ ¬ ¬(r ∈ H ∧ r0 ∈ H ∧ r ≠ null ∧ r0 ≠ null ∧ H[r].nxt = r0);%reflist freely generated by [], +;;%Nil: ⊦ [] + x0 = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]