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Proof step 24 from proof inv-inverts-leq (previous step)

# nσ = ∞, nσ[n0] = nσ[n], ∞.n < n0, ∞.n + 1 < m, n < m, ∞.n < n, ∞.n < m, m < n0, (∞.n + 1) + 1 < n0, n + 1 < n0, n < n0, nσ[n] < nσ[m], ∞.n + 1 < n0, stutf(nσ), ∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0] ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 25:
⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n]

Rule argument

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

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (mon≤(nσ) ↔ true);% ⊦ m < n → m ≤ n; (s)% ⊦ ⌜m⌝ < ∞; (s)% ⊦ m < n → (n ≤ m ↔ false); (s) Used terms: nσ, m, n0