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Proof step 131 from proof rem-stays-reachable-aux2 (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 132:
x = r1 + x0, H[H[r0].nxt].nxt = r0, H[r].nxt = H[r0].nxt, H[r0].nxt ∈ H, r0 ∈ H, path(r0 ' + x + r ', H), r ∈ H ⊦ H[r0].nxt = null, r0 = r, r = H[r0].nxt, H[r0].nxt = r0, r0 = null, r = null, dups(x), r0 ∈ x, r ∈ 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]