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Proof step 14 from proof rem-stays-reachable-aux (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 15:
(r ' + x0).last = H[r].nxt, ce.nxt = H[H[r].nxt].nxt, x0 = r0 + x1, path(r ' + x0, H[r, ce]), H[r].nxt ∈ H[r, ce], r ∈ H, H[r].nxt ∈ H ⊦ H[r].nxt = null, H[r].nxt = ce.nxt, r = null, dups(x0), r ∈ x0, ∃ x. path(H[r].nxt ' + x + H[r].nxt ', H) ∧ ¬ r ∈ x

Rule argument

var: x0

Additional information

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