Theorems · Theorem · commutative algebra
Nat.cast_inj
∀ {R : Type u_1} [inst : AddMonoidWithOne R] [CharZero R] {m n : ℕ}, ↑m = ↑n ↔ m = n- Defined in
- Mathlib.Algebra.CharZero.Defs
- Cited by
- 70 results in Mathlib
- Foundations
- Depth 5 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
- Nat.cast_injectiveproof · cited by 39
Cited by70
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_mulproof · cited by 23
- Nat.cast_eq_zeroproof · cited by 18
- Submodule.finrank_quotient_add_finrankproof · cited by 13
- HasSum.nat_add_negproof · cited by 10
- Submodule.finrank_eq_zeroproof · cited by 9
- Set.ncard_insert_of_notMemproof · cited by 8
- Set.ncard_eq_zeroproof · cited by 7
- Submodule.FG.generators_ncardproof · cited by 7
- Polynomial.degree_comp_neg_Xproof · cited by 7
- Polynomial.natDegree_expandproof · cited by 7
- Polynomial.associated_content_mulproof · cited by 6
- Set.ncard_union_eqproof · cited by 6