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Proof step 11 from proof leninv-zero (previous step)

stutf(nσ), ∀ m. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m - 1))) → m = 0 ⊦ # nσ = ∞ ∧ (⌜n⌝ < # nσ → nσ[n] = 0)

User applied rule cut formula

And obtained the following new goals

Proof step 12:
# nσ = ∞, stutf(nσ), ∀ m. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m - 1))) → m = 0 ⊦ # nσ = ∞ ∧ (⌜n⌝ < # nσ → nσ[n] = 0)
Proof step 18:
stutf(nσ), ∀ m. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m - 1))) → m = 0 ⊦ # nσ = ∞, # nσ = ∞ ∧ (⌜n⌝ < # nσ → nσ[n] = 0)

Rule argument

fma: # nσ = ∞

Additional information

Used formulas: # nσ = ∞