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Proof step 25 from proof rem-stays-reachable-aux1 (previous step)

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

User applied rule exists right

And closed the goal!

Rule argument

pos: right 11 terms: x0 + r0 ' abort: F discard: F computed: F

Additional information

Used simplifier rules: path-butlast: ⊦ path(r ' + x + r0 ', H) → (path(r ' + x, H) ↔ true);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ (r ' + x0 + r0 ').last = r0; (s) Used terms: x0 + r0 '