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Proof step 20 from proof stutf-maxinf-is-fin (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: monle-leq seq: ⊦ mon≤(nσ) ∧ m ≤ n ∧ ⌜n⌝ < # nσ → nσ[m] ≤ nσ[n] subst: [nσ, m, n] → [nσ, n0, n1]

Additional information

Used simplifier rules: stutf-monle: ⊦ stutf(nσ) → (mon≤(nσ) ↔ true);% ⊦ m < n → m ≤ n; (s)% ⊦ ⌜m⌝ < ∞; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ m < n → ¬ n < m; (s) Used terms: nσ, n0, n1