Theorems · Theorem · number theory
Nat.factorial_ne_zero
∀ (n : ℕ), n.factorial ≠ 0
- Defined in
- Mathlib.Data.Nat.Factorial.Basic
- Cited by
- 56 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ne_of_gtproof · cited by 637
- Nat.factorialstatement · cited by 616
- Nat.factorial_posproof · cited by 99
Cited by56
Results whose statement or proof uses this declaration.
- NormedSpace.expSeries_radius_eq_topproof · cited by 27
- Ring.choose_zero_right'proof · cited by 7
- Nat.choose_eq_descFactorial_div_factorialproof · cited by 5
- Ring.choose_natCastproof · cited by 4
- NormedSpace.exp_add_of_commute_of_mem_ballproof · cited by 3
- Ring.choose_negproof · cited by 3
- Real.BohrMollerup.f_nat_eqproof · cited by 2
- PowerSeries.exp_mul_exp_eq_exp_addproof · cited by 2
- sum_range_powproof · cited by 2
- Ring.multichoose_one_right'proof · cited by 2
- isEquivalent_chooseproof · cited by 2