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Proof step 1 from proof sw (conclusion)

⊦ ins≤(a, ins≤(b, x)) = ins≤(b, ins≤(a, x))

User applied rule structural induction

And obtained the following new goals

Proof step 2:
⊦ ins≤(a, ins≤(b, [])) = ins≤(b, ins≤(a, []))
Proof step 8:
∀ a, b. ins≤(a, ins≤(b, x0)) = ins≤(b, ins≤(a, x0)) ⊦ ins≤(a, ins≤(b, a0 + x0)) = ins≤(b, ins≤(a, a0 + x0))

Rule argument

indvar: x

Additional information

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