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Proof step 3 from proof inv-inverts-leq (previous step)

inv(nσ)[nσ[n]] < n, ⌜n⌝ < # nσ, ⌜nσ[n]⌝ < leninv(nσ), stutf(nσ) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ stutf(nσ) → inv(nσ) = (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ ;⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ to leninv(nσ).n)
Proof step 5:
⌜nσ[n]⌝ < leninv(nσ), ⌜n⌝ < # nσ, (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ ;⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ to leninv(nσ).n)[nσ[n]] < n, stutf(nσ) ⊦

Rule argument

spec: <toplevel> name: inv-def seq: ⊦ stutf(nσ) → inv(nσ) = (leninv(nσ) = ∞ ⊃ ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ ; ⌜λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n⌝ to leninv(nσ).n ) subst: [nσ] → [nσ] flags: <all paths>

Additional information

Used terms: nσ