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Proof step 31 from proof add-preserves-reachable (previous step)

H[r1].nxt = H[ce.nxt].nxt, (H[r1].nxt ' + x0).last ∈ H, ce.nxt ∈ H, path(H[r1].nxt ' + x0, H), r1 ∈ H, reachable(H[r1].nxt, r1, H) → reachable(H[r1].nxt, (H[r1].nxt ' + x0).last, H[r1, ce]) ∨ reachable(H[r1].nxt, ce.nxt, H) ⊦ ∃ x. path(H[r1].nxt ' + x, H) ∧ (H[r1].nxt ' + x).last = (H[r1].nxt ' + x0).last, r1 = null, ce.nxt = null, reachable(r1, (H[r1].nxt ' + x0).last, H[r1, ce]), reachable(r1, ce.nxt, H)

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 1 terms: x0

Additional information

Used terms: x0