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Proof step 15 from proof eq-leninv (previous step)

⌜n⌝ < # nσ, stutf(nσ) ⊦ nσ[n] = 0, ⌜nσ[n]⌝ = leninv(nσ) ↔ # nσ = ∞ ∧ (∀ m. n < m ∧ ⌜m⌝ < # nσ → nσ[m] = nσ[n])

User applied rule structural induction

And obtained the following new goals

Proof step 16:
∀ nσ, n. m = nσ[n] ∧ ⌜n⌝ < # nσ ∧ stutf(nσ) → nσ[n] = 0 ∨ (⌜nσ[n]⌝ = leninv(nσ) ↔ # nσ = ∞ ∧ (∀ m. n < m ∧ ⌜m⌝ < # nσ → nσ[m] = nσ[n])), m +1 = nσ[n], ⌜n⌝ < # nσ, stutf(nσ) ⊦ nσ[n] = 0, ⌜nσ[n]⌝ = leninv(nσ) ↔ # nσ = ∞ ∧ (∀ m. n < m ∧ ⌜m⌝ < # nσ → nσ[m] = nσ[n])

Rule argument

term: nσ[n]

Additional information

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