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Proof step 27 from proof inv-inverts-leq (previous step)

nσ[max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]).n] = nσ[n], leninv(nσ) = ∞, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) < # nσ, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]).n < 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 elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 28:
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]) = ∞

Rule argument

spec: nat-inf-basic inst: name: elim seq: ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ) subst: [n∞, m] → [max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]), m0] flags:

Additional information

Used simplifier rules: ⊦ n∞ ≠ ∞ → (n = n∞.n ↔ n∞ = ⌜n⌝ ); (elim) Used terms: max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]), m0