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Proof step 15 from proof frommodified (previous step)

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

User applied rule constructor cut

And closed the goal!

Rule argument

var: x0

Additional information

Used simplifier rules: path-one: ⊦ path(r ', H) ↔ r ∈ H ∧ r ≠ null;%path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H);%reflist freely generated by [], +;;% ⊦ r + x0 = r ' + x0; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; (s)% ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); (s)% ⊦ r ≠ r0 → H[r0, ce][r] = H[r]; (s)% ⊦ x0 + [] = x0; (s)% ⊦ r '.last = r; (s)