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Proof step 16 from proof inv-inverts-leq (previous step)

∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = nσ[n], leninv(nσ) = ∞, ∞.n < n, stutf(nσ), ⌜n⌝ < # nσ ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ stutf(nσ) → (leninv(nσ) = ∞ ↔ # nσ = ∞ ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]))
Proof step 18:
stutf(nσ), ∀ n0. ∃ n1. n0 < n1 ∧ ⌜n1⌝ < # nσ ∧ nσ[n1] = nσ[n], # nσ = ∞ ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0]), ∞.n < n, stutf(nσ), ⌜n⌝ < # nσ ⊦

Rule argument

spec: inst: name: leninv-inf seq: ⊦ stutf(nσ) → ( leninv(nσ) = ∞ ↔ # nσ = ∞ ∧ (∀ m. ∃ m0. m < m0 ∧ nσ[m] < nσ[m0])) subst: [nσ] → [nσ] flags: rewrite, current

Additional information

Used terms: nσ