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

(∀ n. ∃ n0. n < n0 ∧ (∃ m. nσ[m] = n0 - 1 ∧ ¬(∀ m0. m < m0 → nσ[m0] = n0 - 1))) ∨ (∀ n. ¬(n ≠ 0 → (∃ m. nσ[m] = n - 1 ∧ ¬(∀ m0. m < m0 → nσ[m0] = n - 1)))), # nσ = ∞, stutf(nσ) ⊦ ∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# nσ = ∞, stutf(nσ), (∀ n. ∃ n0. n < n0 ∧ (∃ m. nσ[m] = n0 - 1 ∧ ¬(∀ m0. m < m0 → nσ[m0] = n0 - 1))) ∨ (∀ n. ¬(n ≠ 0 → (∃ m. nσ[m] = n - 1 ∧ ¬(∀ m0. m < m0 → nσ[m0] = n - 1)))) ⊦ ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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