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Proof step 49 from proof add-preserves-reachable-rev (previous step)

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

User applied rule constructor cut

And obtained the following new goals

Proof step 50:
H[r1].nxt = H[ce.nxt].nxt, x0 = r + x, path(ce.nxt ' + x0, H[r1, ce]), ce.nxt ∈ H, r1 ∈ H, (ce.nxt ' + x0).last ∈ H[r1, ce] ⊦ (ce.nxt ' + x0).last = ce.nxt, ce.nxt = null, r1 = null, reachable(r1, (ce.nxt ' + x0).last, H), reachable(r1, ce.nxt, H), H[r1].nxt ∈ H ∧ H[r1].nxt ≠ null

Rule argument

var: x0

Additional information

Used simplifier rules: reflist freely generated by [], +;;% ⊦ x0 + [] = x0; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r '.last = r; (s)