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Proof step 8 from proof leninv-zero (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
stutf(nσ), ∀ m. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m - 1 ∧ (# nσ ≠ ∞ ∨ ¬(∀ m1. m0 < m1 → nσ[m1] = m - 1))) → m = 0 ⊦ nσ = ⌜λ n. 0⌝

Rule argument

Additional information

Used simplifier rules: ⊦ ⌜nnf⌝ [n] = nnf(n); (s)% ⊦ ⌜m⌝ < ∞; (s)% ⊦ # ⌜nnf⌝ = ∞; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ m < n → n ≠ 0; (s)