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Proof step 48 from proof add-preserves-reachable-rev (previous step)

H[r1].nxt = H[ce.nxt].nxt, ce.nxt ∈ H, (ce.nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, path(ce.nxt ' + x0, H[r1, ce]) ⊦ ce.nxt = null, r1 = null, (ce.nxt ' + x0).last = ce.nxt, 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 49:
x0 = r + x, H[r1].nxt = H[ce.nxt].nxt, ce.nxt ∈ H, (ce.nxt ' + x0).last ∈ H[r1, ce], r1 ∈ H, path(ce.nxt ' + x0, H[r1, ce]) ⊦ ce.nxt = null, r1 = null, (ce.nxt ' + x0).last = ce.nxt, reachable(r1, ce.nxt, H), reachable(r1, (ce.nxt ' + x0).last, H), H[r1].nxt ∈ H ∧ H[r1].nxt ≠ null

Rule argument

var: x0

Additional information

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