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

# nσ = ∞, stutf(nσ), # nσ = ∞ ∧ stutf(nσ) ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]) → (∃ m1. m0 < nσ[m1]), ∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0] ⊦ ∃ m. m0 + 1 < nσ[m]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# nσ = ∞, stutf(nσ), m0 < nσ[m], ∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0] ⊦ nσ[m] = 0, ∃ m. m0 + 1 < nσ[m]

Rule argument

Additional information

Used simplifier rules: f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1