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Proof step 24 from proof rem-stays-reachable-aux (previous step)

ce.nxt = H[H[r].nxt].nxt, path(ce.nxt ' + x2 + H[r].nxt ', H), r ∈ H, H[r].nxt ∈ H ⊦ H[r].nxt = null, H[r].nxt = ce.nxt, r = ce.nxt, r = null, r = H[r].nxt, dups(x2), ce.nxt ∈ x2, r ∈ x2, H[r].nxt ∈ x2, ∃ x. path(H[r].nxt ' + x + H[r].nxt ', H) ∧ ¬ r ∈ x

User applied rule exists right

And closed the goal!

Rule argument

pos: right 10 terms: ce.nxt ' + x2 abort: F discard: T computed: F

Additional information

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