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Proof step 4 from proof path-last (previous step)

path(r ' + x, H) ⊦ x = [], x.last ∈ H

User applied rule structural induction

And obtained the following new goals

Proof step 5:
∀ r, H. path(r ' + x0, H) → x0 = [] ∨ x0.last ∈ H, path(r ' + (r0 + x0), H) ⊦ r0 + x0 = [], (r0 + x0).last ∈ H

Rule argument

indvar: x

Additional information

Used simplifier rules: reflist freely generated by [], +;;