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Proof step 2 from proof path-trans (previous step)

path(x, H), path(x.last ' + y, H) ⊦ path(x + y, H)

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ H, y. path(x0, H) ∧ path(x0.last ' + y, H) → path(x0 + y, H), path(r + x0, H), path((r + x0).last ' + y, H) ⊦ path((r + x0) + y, H)

Rule argument

indvar: x

Additional information

Used simplifier rules: path-empty: ⊦ ¬ path([], H);%reflist freely generated by [], +;;