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Proof step 12 from proof leninv-zero (previous step)

# nσ = ∞, stutf(nσ), ∀ m. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m - 1))) → m = 0 ⊦ # nσ = ∞ ∧ (⌜n⌝ < # nσ → nσ[n] = 0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
# nσ = ∞, stutf(nσ), ∀ m. (∃ m0. nσ[m0] = m - 1 ∧ ¬(∀ m1. m0 < m1 → nσ[m1] = m - 1)) → m = 0 ⊦ nσ[n] = 0

Rule argument

Additional information

Used simplifier rules: less-inf2: ⊦ ⌜m⌝ < ∞; from specification nat-inf