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

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

User applied rule constructor cut

And obtained the following new goals

Proof step 141:
H[r1].nxt = H[r0].nxt, H[H[r0].nxt].nxt = r0, x = r2 + x0, path(r ' + x2 + r1 ', H), path(r0 ' + x + r1 ', H), path(r ' + (x2 + r1 ') + H[r0].nxt ', H), H[r0].nxt ∈ H, r1 ∈ H, r0 ∈ H ⊦ H[r0].nxt = r1, H[r0].nxt = r0, H[r0].nxt = null, r = r1, r = H[r0].nxt, r0 = r1, r0 = r, r0 = null, r1 = null, dups(x2), dups(x), r1 ∈ x2, r1 ∈ x, r0 ∈ x, r ∈ x2, r0 ∈ x2, H[r0].nxt ∈ x2

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]