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Proof step 28 from proof inv-inverts-leq (previous step)

max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ⌜n1⌝ , nσ[n1] = nσ[n], leninv(nσ) = ∞, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) < # nσ, n1 < n, stutf(nσ), ⌜n⌝ < # nσ, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = nσ[n] → ¬ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) < ⌜m⌝ ⊦ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ∞

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
leninv(nσ) = ∞, nσ[n1] = nσ[n], max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ⌜n1⌝ , ⌜n⌝ < # nσ, stutf(nσ), n1 < n, ⌜n1⌝ < # nσ, ∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = nσ[n] → ¬ n1 < m ⊦

Rule argument

Additional information

Used simplifier rules: less-fin: ⊦ ⌜m⌝ < ⌜n⌝ ↔ m < n; from specification nat-inf%disj: ⊦ ⌜m⌝ ≠ ∞; from specification nat-inf-basic