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Proof step 14 from proof stutf-maxinf-is-fin (previous step)

# nσ = ∞, m0 ≤ n, nσ[m0] ≤ nσ[n], stutf(nσ), m0 ≤ n0, ∀ n1. ∃ n0. n1 < n0 ∧ nσ[n0] = nσ[m0] ⊦ nσ[n0] = nσ[m0]

User applied rule insert lemma

And obtained the following new goals

Proof step 15:
⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n]
Proof step 16:
mon≤(nσ) ∧ m0 ≤ n0 ∧ ⌜n0⌝ < # nσ → nσ[m0] ≤ nσ[n0], # nσ = ∞, m0 ≤ n, nσ[m0] ≤ nσ[n], stutf(nσ), m0 ≤ n0, ∀ n1. ∃ n0. n1 < n0 ∧ nσ[n0] = nσ[m0] ⊦ nσ[n0] = nσ[m0]

Rule argument

spec: inst: name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, m0, n0] flags: current, []

Additional information

Used terms: nσ, m0, n0