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Proof step 4 from proof inv-inverts-leq (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⌜nσ[n]⌝ < leninv(nσ), ⌜n⌝ < # nσ, stutf(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 ⊦

Rule argument

Additional information

Used simplifier rules: to-inf: ⊦ ⌜nnf⌝ to n = ⌜nnf to n⌝ ; from specification stream[natstream]