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Proof step 8 from proof monle-leq (previous step)

nσ[(m1 + 1) + m] < nσ[m1 + m], nσ[m] ≤ nσ[m1 + m], ⌜m1⌝ + ⌜m⌝ < # nσ, nσ[(m1 + 1) + m] < nσ[m], mon≤(nσ), ⌜m1⌝ + ⌜1⌝ + ⌜m⌝ < # nσ ⊦ nσ[m] = 0, nσ[m1 + m] = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ mon≤(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] ≤ nσ[n + 1])
Proof step 10:
nσ[(m1 + 1) + m] < nσ[m1 + m], nσ[m] ≤ nσ[m1 + m], ⌜m1⌝ + ⌜m⌝ < # nσ, nσ[(m1 + 1) + m] < nσ[m], ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] ≤ nσ[n + 1], ⌜m1⌝ + ⌜1⌝ + ⌜m⌝ < # nσ ⊦ nσ[m] = 0, nσ[m1 + m] = 0

Rule argument

spec: inst: name: monle-def seq: ⊦ mon≤(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] ≤ nσ[n + 1]) subst: [nσ] → [nσ] flags: rewrite, current

Additional information

Used terms: nσ