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Proof step 3 from proof ole-in (previous step)

b < a, ordered≤(a ' + x), b ∈ x ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 4:
b < a, ordered≤(a ' + (a0 + x0)), b ∈ a0 + x0, ∀ b, a. ¬(b < a ∧ ordered≤(a ' + x0) ∧ b ∈ x0) ⊦

Rule argument

indvar: x

Additional information

Used simplifier rules: list freely generated by [], +;;% ⊦ ¬ a ∈ []; (s)