Theorems · Theorem · commutative algebra
AddGroupWithOne.intCast_ofNat
∀ {R : Type u} [self : AddGroupWithOne R] (n : ℕ), IntCast.intCast ↑n = ↑nThe canonical homomorphism ℤ → R agrees with the one from ℕ → R on ℕ.
- Defined in
- Mathlib.Data.Int.Cast.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- AddGroupWithOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupWithOnestatement and proof · cited by 111
Cited by8
Results whose statement or proof uses this declaration.
- Int.cast_natCastproof · cited by 393
- Int.cast_zeroproof · cited by 188
- Int.cast_ofNatproof · cited by 86
- AddGroupWithOne.extproof · cited by 2
- Function.Surjective.addCommGroupWithOneproof · cited by 0
- Function.Surjective.ringproof · cited by 0
- Function.Injective.addCommGroupWithOneproof · cited by 0
- Function.Injective.ringproof · cited by 0