Theorems · Theorem · number theory
IsUnit.natCast_factorial_of_le
∀ {A : Type u_1} [inst : Semiring A] {n : ℕ}, IsUnit ↑n.factorial → ∀ {m : ℕ}, m ≤ n → IsUnit ↑m.factorial- Defined in
- Mathlib.Data.Nat.Factorial.NatCast
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- add_zeroproof · cited by 2,707
- IsUnitstatement and proof · cited by 1,602
- add_assocproof · cited by 746
- Nat.factorialstatement and proof · cited by 616
- Nat.cast_mulproof · cited by 309
- add_right_commproof · cited by 85
- ExistsAddOfLE.exists_add_of_leproof · cited by 42
- Nat.factorial_succproof · cited by 30
- Nat.cast_commuteproof · cited by 24
- Commute.isUnit_mul_iffproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- IsUnit.natCast_factorial_of_ltproof · cited by 3
- Nat.castChoose_eqproof · cited by 1