Theorems · Theorem · number theory
Nat.self_le_factorial
∀ (n : ℕ), n ≤ n.factorial
- Defined in
- Mathlib.Data.Nat.Factorial.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.factorialstatement and proof · cited by 616
- Nat.factorial_posproof · cited by 99
Cited by7
Results whose statement or proof uses this declaration.
- Nat.add_factorial_succ_lt_factorial_add_succproof · cited by 3
- LiouvilleNumber.summableproof · cited by 2
- Nat.lt_factorial_selfproof · cited by 1
- Nat.coprimes_ltproof · cited by 1
- alternatingGroup.nontrivial_of_three_le_cardproof · cited by 1
- factorial_tendsto_atTopproof · cited by 0
- Nat.add_factorial_le_factorial_addproof · cited by 0