Theorems · Theorem · number theory
Nat.factorial_le
∀ {m n : ℕ}, m ≤ n → m.factorial ≤ n.factorial- Defined in
- Mathlib.Data.Nat.Factorial.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
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.
- Nat.factorialstatement · cited by 616
- Nat.factorial_posproof · cited by 99
- Nat.factorial_dvd_factorialproof · cited by 6
Cited by10
Results whose statement or proof uses this declaration.
- Nat.factorial_ltproof · cited by 3
- Nat.add_factorial_succ_lt_factorial_add_succproof · cited by 3
- Equiv.Perm.alternatingGroup_le_of_isPreprimitive_of_isThreeCycle_memproof · cited by 2
- spectrum.exp_mem_expproof · cited by 1
- Equiv.Perm.subgroup_eq_top_of_isPreprimitive_of_isSwap_memproof · cited by 1
- Nat.eventually_pow_lt_factorial_subproof · cited by 1
- Complex.norm_exp_sub_sum_le_norm_mul_expproof · cited by 0
- factorial_tendsto_atTopproof · cited by 0
- Equiv.Perm.subgroup_eq_top_of_nontrivialproof · cited by 0
- Nat.monotone_factorialproof · cited by 0