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Proof step 7 from proof inv-inverts-leq (previous step)

leninv(nσ) = ∞, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]).n < n, stutf(nσ), ⌜n⌝ < # nσ ⊦

User applied rule insert lemma

And obtained the following new goals

Proof step 8:
⊦ (max∞(np) = ∞ ⊃ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n));(∃ n. np(max∞(np).n)) ∧ (∀ m. np(m) → ¬ max∞(np) < ⌜m⌝ ))
Proof step 9:
(max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ∞ ⊃ (∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = nσ[n]) ∨ (∀ n0. ¬(⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n])) ; (∃ n0. ⌜max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]).n⌝ < # nσ ∧ nσ[max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]).n] = nσ[n]) ∧ (∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = nσ[n] → ¬ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) < ⌜m⌝ ) ), leninv(nσ) = ∞, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]).n < n, stutf(nσ), ⌜n⌝ < # nσ ⊦

Rule argument

spec: inst: name: maxinf-def seq: ⊦ (max∞(np) = ∞ ⊃ (∀ n. ∃ n0. n < n0 ∧ np(n0)) ∨ (∀ n. ¬ np(n)) ;(∃ n. np(max∞(np).n)) ∧ (∀ m. np(m) → ¬ max∞(np) < ⌜m⌝ ) ) subst: [np] → [λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]] flags: current, []

Additional information

Used terms: λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]