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Proof step 21 from proof stutf-maxinf-is-fin (previous step)

∀ n. ∃ n0. n < n0 ∧ ⌜n0⌝ < # nσ ∧ nσ[n0] = m, stutf(nσ) ⊦ # nσ = ∞, # nσ = ∞ ∧ (∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m) ∨ (∀ n. ⌜n⌝ < # nσ → nσ[n] < m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 22:
⌜n⌝ < # nσ, stutf(nσ), m ≤ nσ[n], ∀ n. ∃ n0. n < n0 ∧ ⌜n0⌝ < # nσ ∧ nσ[n0] = m ⊦ # nσ = ∞

Rule argument

Additional information

Used simplifier rules: lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat