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

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
# nσ = ∞, stutf(nσ) ⊦ (∃ m. nσ[m] = n ∧ ¬(∀ m0. m < m0 → nσ[m0] = nσ[m])) ∧ (∀ m. (m ≠ 0 → (∃ m0. nσ[m0] = m - 1 ∧ ¬(∀ m1. m0 < m1 → nσ[m1] = m - 1))) → ¬ n + 1 < m) ↔ (∃ m. nσ[m] = n ∧ (∀ m0. m < m0 → nσ[m0] = nσ[m] + 1))

Rule argument

Additional information

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