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Proof step 52 from proof inv-inverts (previous step)

nσ[n + 1] = nσ[n] + 1, max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) = ⌜n0⌝ , ⌜n⌝ + ⌜1⌝ < # 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, n0 = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 53:
⊦ max∞(np) = ⌜n⌝ ↔ np(n) ∧ (∀ m. np(m) → ¬ n < m)
Proof step 54:
nσ[n + 1] = nσ[n] + 1, (⌜n0⌝ < # nσ ∧ nσ[n0] = nσ[n]) ∧ (∀ m. ⌜m⌝ < # nσ ∧ nσ[m] = nσ[n] → ¬ n0 < m), ⌜n⌝ + ⌜1⌝ < # 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, n0 = n

Rule argument

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

Additional information

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