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Proof step 47 from proof inv-ls-succ (previous step)

leninv(nσ) = ⌜n1⌝ , max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1) = ∞, 1 + n < n1, stutf(nσ), ∞.n ≤ ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n1)[n] ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ leninv(nσ) = max∞(λ n. n ≠ 0 → (∃ m. ⌜m⌝ < # nσ ∧ nσ[m] = n - 1 ∧ ¬(# nσ = ∞ ∧ (∀ m0. m < m0 → nσ[m0] = n - 1))))
Proof step 49:
max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1) = ∞, max∞(λ n. n ≠ 0 → (∃ m. ⌜m⌝ < # nσ ∧ nσ[m] = n - 1 ∧ ¬(# nσ = ∞ ∧ (∀ m0. m < m0 → nσ[m0] = n - 1)))) = ⌜n1⌝ , 1 + n < n1, stutf(nσ), ∞.n ≤ ((λ m. max∞(λ n. ⌜n⌝ < # nσ ∧ nσ[n] = m).n) to n1)[n] ⊦

Rule argument

spec: <toplevel> name: leninv-def seq: ⊦ leninv(nσ) = max∞ (λ n. n ≠ 0 → (∃ m. ⌜m⌝ < # nσ ∧ nσ[m] = n - 1 ∧ ¬ (# nσ = ∞ ∧ (∀ m0. m < m0 → nσ[m0] = n - 1)))) subst: [nσ] → [nσ] flags: <all paths>

Additional information

Used terms: nσ