Theorems · Theorem · number theory
Nat.factorial_lt
∀ {m n : ℕ}, 0 < n → (n.factorial < m.factorial ↔ n < m)- Defined in
- Mathlib.Data.Nat.Factorial.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- not_leproof · cited by 328
- lt_transproof · cited by 165
- Nat.factorial_posproof · cited by 99
- Nat.factorial_succproof · cited by 30
- Nat.factorial_leproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- Nat.one_lt_factorialproof · cited by 2
- Nat.factorial_injproof · cited by 1
- Nat.factorial_lt_of_ltproof · cited by 0