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Proof step 179 from proof rem-stays-reachable-aux2 (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 180:
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

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