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Proof step 84 from proof inv-ls-succ (previous step)

⌜m⌝ < # nσ, n < nσ[m], stutf(nσ), ∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, ∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ n + 1, ∀ m0. (∃ m1. ⌜m1⌝ < # nσ ∧ nσ[m1] = m0 - 1) → ¬ nσ[m] + 1 < m0 ⊦ # nσ = ∞

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 85:
⊦ n∞ = ∞ ↔ ¬(∃ n. n∞ = ⌜n⌝ )
Proof step 86:
n < nσ[m], ⌜m⌝ < # nσ, stutf(nσ), ∞.n ≤ max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n).n, ∀ m0. (∃ m1. ⌜m1⌝ < # nσ ∧ nσ[m1] = m0 - 1) → ¬ nσ[m] + 1 < m0, ∀ n0. ¬ ⌜n0⌝ < # nσ ∨ nσ[n0] ≠ n + 1 ⊦ ∀ n. # nσ ≠ ⌜n⌝

Rule argument

spec: nat-inf name: notinf-fin seq: ⊦ n∞ = ∞ ↔ ¬(∃ n. n∞ = ⌜n⌝ ) subst: [n∞] → [# nσ] flags: <all paths>

Additional information

Used terms: # nσ