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Proof step 18 from proof removed-stays-reachable (previous step)

ce.nxt = H[H[r0].nxt].nxt, r0 ∈ H, H[r0].nxt ∈ H, reachable(r, r0, H), path(r ' + x + H[r0].nxt ', H) ⊦ ∃ r1. reachable(r, r1, H) ∧ H[r0].nxt = H[r1].nxt ∧ ¬ reachable(r0, r1, H), ∃ x0. path(r ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0, H[r0].nxt = null, H[r0].nxt = ce.nxt, r0 = r, r = H[r0].nxt, r0 ∈ x, reachable(ce.nxt, H[r0].nxt, H) ∧ ¬ reachable(ce.nxt, r0, H), ∃ r1. reachable(r, r1, H) ∧ H[r1].nxt = H[r0].nxt ∧ ¬ reachable(r0, r1, H), ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: x

Additional information

Used simplifier rules: a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used terms: x