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

ordered≤(x + a ') ⊦ ordered≤(x + a ' + b ') ↔ ¬ b < a

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: x

Additional information

Used simplifier rules: ole-two: ⊦ ordered≤(a ' + b ') ↔ ¬ b < a;%list freely generated by [], +;;%Nil: ⊦ [] + x = x; from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list