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Proof step 3 from proof monls-notsmall (previous step)

nσ[0] = 0, nσ[1] = 0, mon<(nσ) ⊦ # nσ = ⌜1⌝ , nσ = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ mon<(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1])
Proof step 5:
nσ[0] = 0, nσ[1] = 0, ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1] ⊦ # nσ = ⌜1⌝ , nσ = []

Rule argument

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

Additional information

Used terms: nσ