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Proof step 5 from proof id-reachable (previous step)

H[r].nxt = null, (r ' + x).last ∈ H, path(r ' + x, H) ⊦ r = (r ' + x).last, (r ' + x).last = null

User applied rule constructor cut

And closed the goal!

Rule argument

var: x

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%null-not-start-of-path: ⊦ ¬ path(null ' + x, H);%reflist freely generated by [], +;;%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]