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Proof step 96 from proof inv-ls-succ (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 97:
⊦ n∞ = ∞ ↔ ¬(∃ n. n∞ = ⌜n⌝ )
Proof step 98:
⌜n⌝ + ⌜1⌝ < leninv(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⌝ )[n + 1] ≤ (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⌝ )[n] ⊦ ∀ n0. max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1) ≠ ⌜n0⌝

Rule argument

spec: nat-inf name: notinf-fin seq: ⊦ n∞ = ∞ ↔ ¬(∃ n. n∞ = ⌜n⌝ ) subst: [n∞] → [max∞(λ n0. ⌜n0⌝ < # nσ ∧ nσ[n0] = n + 1)] flags: <all paths>

Additional information

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