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

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

User applied rule constructor cut

And obtained the following new goals

Proof step 181:
H[r].nxt = H[r1].nxt, x = r0 + x0, path(H[H[r1].nxt].nxt ' + x3 + r1 ', H), path(r1 ' + x + r ', H), r1 ∈ H, r ∈ H, H[r1].nxt ∈ H ⊦ H[r1].nxt = r1, H[r1].nxt = H[H[r1].nxt].nxt, H[r1].nxt = null, r = H[H[r1].nxt].nxt, r = null, r1 = r, r1 = H[H[r1].nxt].nxt, dups(x), dups(x3), r ∈ x, r1 ∈ x3, H[r1].nxt ∈ x3, r1 ∈ x, r ∈ x3, H[H[r1].nxt].nxt ∈ x3

Rule argument

var: x

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 [], +;;% ⊦ [] + x0 = x0; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]