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Proof step 27 from proof add-preserves-reachable-rev (previous step)

H[r1].nxt = H[ce.nxt].nxt, path(H[r].nxt ' + x, H[r1, ce]), reachable(r1, H[r].nxt, H), r1 ∈ H, ce.nxt ∈ H, r ∈ H ⊦ x.last = ce.nxt, ce.nxt = null, r = r1, r = null, r1 = null, x = [], reachable(r1, ce.nxt, H), reachable(r1, x.last, H), H[H[r].nxt].nxt ≠ null ∧ H[H[r].nxt].nxt ∈ H

User applied rule constructor cut

And obtained the following new goals

Proof step 28:
H[r1].nxt = H[ce.nxt].nxt, x = r0 + x0, path(H[r].nxt ' + x, H[r1, ce]), reachable(r1, H[r].nxt, H), r ∈ H, ce.nxt ∈ H, r1 ∈ H ⊦ x.last = ce.nxt, ce.nxt = null, r = null, r = r1, r1 = null, x = [], reachable(r1, x.last, H), reachable(r1, ce.nxt, H), H[H[r].nxt].nxt ≠ null ∧ H[H[r].nxt].nxt ∈ H

Rule argument

var: x

Additional information

Used simplifier rules: reflist freely generated by [], +;;