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Proof step 2 from proof ole-in (previous step)

b ∈ x, ordered≤(a ' + x), b < a ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 3:
∀ b, a. ¬(b ∈ x0 ∧ ordered≤(a ' + x0) ∧ b < a), b ∈ a0 + x0, ordered≤(a ' + (a0 + x0)), b < a ⊦

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;%in-empty: ⊦ ¬ a ∈ []; from specification list