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Proof step 3 from proof ordered-prefix (previous step)

ordered≤(x0), x ⊑ x0 ⊦ ordered≤(x)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
ordered≤(x0), a + x1 ⊑ x0, ∀ x0. ordered≤(x0) ∧ x1 ⊑ x0 → ordered≤(x1) ⊦ ordered≤(a + x1)

Rule argument

indvar: x

Additional information

Used simplifier rules: le-e: ⊦ ordered≤([]);%list freely generated by [], +;;% ⊦ [] ⊑ x; (s)