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Proof step 111 from proof inv-get-inverse-between (previous step)

# nσ = ∞, nσ[n1] < nσ[m1], n1 + m + 1 < max∞(λ n0. nσ[n0] = nσ[n1] + 1).n, stutf(nσ), ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1, ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m ⊦ nσ[n1 + m + 1] = nσ[n1] + 1

User applied rule cut formula

And obtained the following new goals

Proof step 112:
# nσ = ∞, max∞(λ n0. nσ[n0] = nσ[n1] + 1) = ∞, n1 + m + 1 < max∞(λ n0. nσ[n0] = nσ[n1] + 1).n, nσ[n1] < nσ[m1], stutf(nσ), ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m, ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1 ⊦ nσ[n1 + m + 1] = nσ[n1] + 1
Proof step 123:
# nσ = ∞, n1 + m + 1 < max∞(λ n0. nσ[n0] = nσ[n1] + 1).n, nσ[n1] < nσ[m1], stutf(nσ), ∀ m. nσ[m] = nσ[n1] → ¬ n1 < m, ∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1 ⊦ nσ[n1 + m + 1] = nσ[n1] + 1, max∞(λ n0. nσ[n0] = nσ[n1] + 1) = ∞

Rule argument

fma: max∞(λ n0. nσ[n0] = nσ[n1] + 1) = ∞

Additional information

Used formulas: max∞(λ n0. nσ[n0] = nσ[n1] + 1) = ∞