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Proof step 1 from proof monls-exists-maxls (conclusion)

mon<(nσ), nσ[0] ≤ n, n < nσ[m], ⌜m⌝ < # nσ ⊦ ∃ m0. nσ[m0] ≤ n ∧ n < nσ[m0 + 1] ∧ m0 ≤ m

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ nσ, n. mon<(nσ) ∧ nσ[0] ≤ n ∧ n < nσ[m0] ∧ ⌜m0⌝ < # nσ → (∃ m1. nσ[m1] ≤ n ∧ n < nσ[m1 + 1] ∧ m1 ≤ m0), mon<(nσ), nσ[0] ≤ n, n < nσ[m0 +1], ⌜m0 +1⌝ < # nσ ⊦ ∃ m1. nσ[m1] ≤ n ∧ n < nσ[m1 + 1] ∧ m1 ≤ m0 +1

Rule argument

indvar: m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;%ls-le-simp: ⊦ m < n → (n ≤ m ↔ false); from specification nat