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Proof step 51 from proof reachable-addnew-rev (previous step)

path(H[r].nxt ' + x0, H[H[r].nxt, ce]), r ∈ H, (H[r].nxt ' + x0).last ∈ H ⊦ H[r].nxt = null, r = H[r].nxt, r = null, dups(x0), reachable(r, (H[r].nxt ' + x0).last, H), reachable(ce.nxt, (H[r].nxt ' + x0).last, H), H[r].nxt ∈ H, r ∈ x0, H[r].nxt ∈ x0

User applied rule constructor cut

And obtained the following new goals

Proof step 52:
x0 = r0 + x, path(H[r].nxt ' + x0, H[H[r].nxt, ce]), (H[r].nxt ' + x0).last ∈ H, r ∈ H ⊦ H[r].nxt = null, r = null, r = H[r].nxt, dups(x0), reachable(ce.nxt, (H[r].nxt ' + x0).last, H), reachable(r, (H[r].nxt ' + x0).last, H), H[r].nxt ∈ x0, r ∈ x0, H[r].nxt ∈ H

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)