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Proof step 7 from proof null-not-reachable (previous step)

x.last = null, path(r ' + x, H), null ∈ H ⊦ x = []

User applied rule structural induction

And obtained the following new goals

Proof step 8:
∀ r, H. x0.last = null ∧ path(r ' + x0, H) ∧ null ∈ H → x0 = [], (r0 + x0).last = null, path(r ' + (r0 + x0), H), null ∈ H ⊦ r0 + x0 = []

Rule argument

indvar: x

Additional information

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