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Proof step 44 from proof inv-get-inverse-last (previous step)

max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n) = ⌜n1⌝ , ⌜n1⌝ + ⌜m⌝ + ⌜1⌝ < # nσ, stutf(nσ), (# nσ = ∞ ⊃ nσ[m1] = n ∧ (∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1);nσ[(# nσ).n - 1] = n) ⊦ nσ[n1 + m + 1] = n + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 45:
⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m)
Proof step 46:
(⌜n1⌝ < # nσ ∧ nσ[n1] = n) ∧ (∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = n → ¬ n1 < m), ⌜n1⌝ + ⌜m⌝ + ⌜1⌝ < # nσ, stutf(nσ), (# nσ = ∞ ⊃ nσ[m1] = n ∧ (∀ m0. m1 < m0 → nσ[m0] = nσ[m1] + 1);nσ[(# nσ).n - 1] = n) ⊦ nσ[n1 + m + 1] = n + 1

Rule argument

spec: inst: name: maxinf-fin seq: ⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m) subst: [n, np] → [n1, λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n] flags: rewrite, current

Additional information

Used terms: n1, λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n