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Proof step 32 from proof inv-inverts-last (previous step)

nσ[n] < n1, # nσ = ⌜n⌝ + ⌜1⌝ , leninv(nσ) = ⌜n1⌝ , stutf(nσ) ⊦ max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = nσ[n]).n = n

User applied rule cut formula

And obtained the following new goals

Proof step 33:
max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ∞, nσ[n] < n1, # nσ = ⌜n⌝ + ⌜1⌝ , leninv(nσ) = ⌜n1⌝ , stutf(nσ) ⊦ max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = nσ[n]).n = n
Proof step 40:
nσ[n] < n1, # nσ = ⌜n⌝ + ⌜1⌝ , leninv(nσ) = ⌜n1⌝ , stutf(nσ) ⊦ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ∞, max∞(λ n0. ¬ n < n0 ∧ nσ[n0] = nσ[n]).n = n

Rule argument

fma: max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ∞

Additional information

Used formulas: max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ∞