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Proof step 2 from proof path-last-nxt (previous step)

path(r ' + x + r0 ', H) ⊦ H[(r ' + x).last].nxt = r0

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ r, r0, H. path(r ' + x0 + r0 ', H) → H[(r ' + x0).last].nxt = r0, path(r ' + (r1 + x0) + r0 ', H) ⊦ H[(r ' + (r1 + x0)).last].nxt = r0

Rule argument

indvar: x

Additional information

Used simplifier rules: path-two: ⊦ path(r ' + r0 ', H) ↔ ¬ ¬(r ∈ H ∧ r0 ∈ H ∧ r ≠ null ∧ r0 ≠ null ∧ H[r].nxt = r0);%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]%Nil: ⊦ [] + x0 = x0; from specification list[reflist]