Theorems · Theorem · commutative algebra
Nat.cast_injective
∀ {R : Type u_1} [inst : AddMonoidWithOne R] [CharZero R], Function.Injective Nat.cast- Defined in
- Mathlib.Algebra.CharZero.Defs
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- AddMonoidWithOneCharZero
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.
- CharZerostatement and proof · cited by 932
- AddMonoidWithOnestatement and proof · cited by 313
- CharZero.cast_injectiveproof · cited by 6
Cited by40
Results whose statement or proof uses this declaration.
- Nat.cast_injproof · cited by 70
- Nat.castEmbeddingproof · cited by 29
- Nat.strictMono_castproof · cited by 12
- HurwitzKernelBounds.summable_f_natproof · cited by 5
- HasProd.of_nat_of_neg_add_oneproof · cited by 5
- HasSum.nat_add_neg_add_oneproof · cited by 5
- HasSum.of_nat_of_neg_add_oneproof · cited by 5
- pow_ne_of_irreducible_X_pow_sub_Cproof · cited by 4
- CharZero.of_moduleproof · cited by 4
- Cardinal.toENatAux_natproof · cited by 4
- Nat.exists_add_mul_eq_of_gcd_dvd_of_mul_pred_leproof · cited by 3
- CharP.char_ne_zero_of_finiteproof · cited by 3