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Proof step 7 from proof stutf-maxinf-is-fin (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 8:
# nσ = ∞, ∀ n. ∃ n0. n < n0 ∧ ⌜n0⌝ < # nσ ∧ nσ[n0] = m, stutf(nσ) ⊦ # nσ = ∞ ∧ (∃ n. ∀ n0. ¬ n0 < n → nσ[n0] = m) ∨ (∀ n. ⌜n⌝ < # nσ → nσ[n] < m)
Proof step 21:
∀ 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)

Rule argument

fma: # nσ = ∞

Additional information

Used formulas: # nσ = ∞