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Proof step 21 from proof rem-stays-reachable-aux1 (previous step)

path(H[H[r0].nxt].nxt ' + x0 + (r0 ' + x) + H[r0].nxt ', H), path((r0 ' + x) + H[r0].nxt ', H), H[r0].nxt ∈ H, r0 ∈ H ⊦ H[r0].nxt = r0, H[H[r0].nxt].nxt = r0, H[r0].nxt = null, H[r0].nxt = H[H[r0].nxt].nxt, dups(x), dups(x0), dups(x0 + x), reachable(H[H[r0].nxt].nxt, r0, H), r0 ∈ x, r0 ∈ x0, H[r0].nxt ∈ x, H[r0].nxt ∈ x0, H[H[r0].nxt].nxt ∈ x, H[H[r0].nxt].nxt ∈ x0, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

User applied rule constructor cut

And obtained the following new goals

Proof step 22:
x = [], path((r0 ' + x) + H[r0].nxt ', H), path(H[H[r0].nxt].nxt ' + x0 + (r0 ' + x) + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H ⊦ H[r0].nxt = H[H[r0].nxt].nxt, H[r0].nxt = null, H[H[r0].nxt].nxt = r0, H[r0].nxt = r0, dups(x0 + x), dups(x0), dups(x), reachable(H[H[r0].nxt].nxt, r0, H), H[H[r0].nxt].nxt ∈ x0, H[H[r0].nxt].nxt ∈ x, H[r0].nxt ∈ x0, H[r0].nxt ∈ x, r0 ∈ x0, r0 ∈ x, ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Rule argument

var: x

Additional information

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