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Proof step 3 from proof path-butlast (previous step)

path(r ' + x + r0 ', H) ⊦ path(r ' + x, H)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
path(r ' + (r1 + x0) + r0 ', H), ∀ r, r0, H. path(r ' + x0 + r0 ', H) → path(r ' + x0, H) ⊦ path(r ' + (r1 + x0), H)

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;%path-one: ⊦ path(r ', H) ↔ r ∈ H ∧ r ≠ null;%reflist freely generated by [], +;;% ⊦ [] + x0 = x0; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ x0 + [] = x0; (s)