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Proof step 90 from proof leninv-succ (previous step)

stutf(nσ) ⊦ # nσ = ∞, (∃ m. ⌜m⌝ < # nσ ∧ nσ[m] = n) ∧ (∀ m. (m ≠ 0 → (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m - 1)) → ¬ n + 1 < m) ↔ nσ[(# nσ).n - 1] = n

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 91:
⊦ n∞ ≠ ∞ ↔ (∃ n. n∞ = ⌜n⌝ )
Proof step 92:
stutf(nσ) ⊦ ∀ n. # nσ ≠ ⌜n⌝ , (∃ m. ⌜m⌝ < # nσ ∧ nσ[m] = n) ∧ (∀ m. (m ≠ 0 → (∃ m0. ⌜m0⌝ < # nσ ∧ nσ[m0] = m - 1)) → ¬ n + 1 < m) ↔ nσ[(# nσ).n - 1] = 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