Theorems · Theorem · commutative algebra
CharP.isUnit_natCast_iff
∀ {R : Type u_1} [inst : Ring R] {p : ℕ} [CharP R p] {n : ℕ}, Nat.Prime p → (IsUnit ↑n ↔ ¬p ∣ n)- Defined in
- Mathlib.Algebra.CharP.Invertible
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Nontrivialproof · cited by 2,416
- Nat.Primestatement and proof · cited by 2,059
- IsUnitstatement and proof · cited by 1,602
- CharPstatement and proof · cited by 478
- Nat.Prime.ne_oneproof · cited by 61
- CharP.cast_eq_zero_iffproof · cited by 42
- IsUnit.ne_zeroproof · cited by 36
- isUnit_of_invertibleproof · cited by 26
- CharP.nontrivial_of_char_ne_oneproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- CharP.isUnit_intCast_iffproof · cited by 0
- IsUnit.natCast_factorial_iff_of_charPproof · cited by 0
- CharP.isUnit_ofNat_iffproof · cited by 0