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Proof step 1 from proof orderedle-all (conclusion)

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

User applied rule structural induction

And obtained the following new goals

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

Rule argument

indvar: x

Additional information

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