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

path(x, H) ⊦ path(x, H -- r), r ∈ x

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ H, r. path(x0, H) → path(x0, H -- r) ∨ r ∈ x0, path(r0 + x0, H) ⊦ path(r0 + x0, H -- r), r ∈ r0 + x0

Rule argument

indvar: x

Additional information

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