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Proof step 10 from proof inv-inverts-leq (previous step)

leninv(nσ) = ∞, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]).n < n, stutf(nσ), ⌜n⌝ < # nσ, (max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ∞ ⊃ (∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = nσ[n]) ∨ (∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ nσ[n]) ; max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) < # nσ ∧ nσ[max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]).n] = nσ[n] ∧ (∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = nσ[n] → ¬ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) < ⌜m⌝ ) ) ⊦

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: left 5

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