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Proof step 10 from proof monls-notsmall (previous step)

nσ[0] = 0, n0 < nσ[n0 + 1], ⌜n0⌝ + ⌜1⌝ < # nσ, ⌜2⌝ + ⌜n0⌝ < # nσ, mon<(nσ), nσ[2 + n0] ≤ nσ[n0 + 1], nσ[2 + n0] ≤ n0 + 1 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ mon<(nσ) ↔ (∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1])
Proof step 12:
nσ[0] = 0, ⌜2⌝ + ⌜n0⌝ < # nσ, ⌜n0⌝ + ⌜1⌝ < # nσ, n0 < nσ[n0 + 1], nσ[2 + n0] ≤ n0 + 1, nσ[2 + n0] ≤ nσ[n0 + 1], ∀ n. ⌜n⌝ + ⌜1⌝ < # nσ → nσ[n] < nσ[n + 1] ⊦

Rule argument

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

Additional information

Used terms: nσ