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Proof step 4 from proof leninv-inf-strong (previous step)

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

User applied rule structural induction

And obtained the following new goals

Proof step 5:
# nσ = ∞, stutf(nσ), ∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0] ⊦ ∃ m0. 0 < nσ[m0]
Proof step 9:
∀ nσ. # nσ = ∞ ∧ stutf(nσ) ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]) → (∃ m1. m0 < nσ[m1]), # nσ = ∞, stutf(nσ), ∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0] ⊦ ∃ m1. m0 +1 < nσ[m1]

Rule argument

indvar: m

Additional information

Used simplifier rules: nat freely generated by 0, +1;;