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Proof step 1 from proof orderedls-all (conclusion)

⊦ ordered<(x) ↔ (∀ m, n. m < n ∧ n < # x → x[m] < x[n])

User applied rule structural induction

And obtained the following new goals

Proof step 2:
ordered<(x0) ↔ (∀ m, n. m < n ∧ n < # x0 → x0[m] < x0[n]) ⊦ ordered<(a + x0) ↔ (∀ m, n. m < n ∧ n < #(a + x0) → (a + x0)[m] < (a + x0)[n])

Rule argument

indvar: x

Additional information

Used simplifier rules: ls-e: ⊦ ordered<([]);%list freely generated by [], +;;%size-01: ⊦ # [] = 0; from specification list-data%less-1: ⊦ ¬ n < 0; from specification nat-basic1