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Proof step 83 from proof inv-ls-succ (previous step)

∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, n < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), ∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ n + 1, ∀ m2. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m2 - 1) → ¬ nσ[m] + 1 < m2 ⊦ # nσ = ∞

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 84:
⊦ n∞ ≠ ∞ ↔ (∃ n. n∞ = ⌜n⌝ )
Proof step 85:
∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, n < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), ∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ n + 1, ∀ m2. (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m2 - 1) → ¬ nσ[m] + 1 < m2 ⊦ ∀ n. # nσ ≠ ⌜n⌝

Rule argument

spec: nat-inf-basic inst: name: notinf-fin seq: ⊦ n∞ ≠ ∞ ↔ (∃ n. n∞ = ⌜n⌝ ) subst: [n∞] → [# nσ] flags: rewrite

Additional information

Used terms: # nσ