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Proof step 26 from proof add-preserves-reachable-rev (previous step)

H[r1].nxt = H[ce.nxt].nxt, reachable(r1, H[r].nxt, H), r1 ∈ H, ce.nxt ∈ H, path(H[r].nxt ' + x, H[r1, ce]), r ∈ H ⊦ r1 = null, ce.nxt = null, r = r1, x = [], r = null, x.last = ce.nxt, 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 27:
x = r0 + x0, H[r1].nxt = H[ce.nxt].nxt, reachable(r1, H[r].nxt, H), r1 ∈ H, ce.nxt ∈ H, path(H[r].nxt ' + x, H[r1, ce]), r ∈ H ⊦ r1 = null, ce.nxt = null, r = r1, x = [], r = null, x.last = ce.nxt, reachable(r1, ce.nxt, H), reachable(r1, x.last, 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 [], +;;