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Proof step 2 from proof leninv-inf (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ leninv(nσ) = max∞(λ n. n ≠ 0 → (∃ m. ⌜m⌝ < # nσ ∧ nσ[m] = n - 1 ∧ ¬(# nσ = ∞ ∧ (∀ m0. m < m0 → nσ[m0] = n - 1))))
Proof step 4:
stutf(nσ) ⊦ max∞(λ n. n ≠ 0 → (∃ m. ⌜m⌝ < # nσ ∧ nσ[m] = n - 1 ∧ ¬(# nσ = ∞ ∧ (∀ m0. m < m0 → nσ[m0] = n - 1)))) = ∞ ↔ # nσ = ∞ ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0])

Rule argument

spec: inst: name: leninv-def seq: ⊦ leninv(nσ) = max∞ (λ n. n ≠ 0 → (∃ m. ⌜m⌝ < # nσ ∧ nσ[m] = n - 1 ∧ ¬(# nσ = ∞ ∧ (∀ m0. m < m0 → nσ[m0] = n - 1)))) subst: [nσ] → [nσ] flags: rewrite, current

Additional information

Used terms: nσ