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Proof step 9 from proof monle-leq (previous step)

⌜m1⌝ + ⌜1⌝ + ⌜m⌝ < # nσ, nσ[(m1 + 1) + m] < nσ[m], ⌜m1⌝ + ⌜m⌝ < # nσ, nσ[(m1 + 1) + m] < nσ[m1 + m], mon≤(nσ), nσ[m] ≤ nσ[m1 + m] ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ mon≤(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] ≤ nσ[n + 1])
Proof step 11:
nσ[(m1 + 1) + m] < nσ[m1 + m], ⌜m1⌝ + ⌜m⌝ < # nσ, nσ[(m1 + 1) + m] < nσ[m], ⌜m1⌝ + ⌜1⌝ + ⌜m⌝ < # nσ, nσ[m] ≤ nσ[m1 + m], ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] ≤ nσ[n + 1] ⊦

Rule argument

spec: <toplevel> name: monle-def seq: ⊦ mon≤(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] ≤ nσ[n + 1]) subst: [nσ] → [nσ] flags: <all paths>

Additional information

Used terms: nσ