Theorems · Theorem · commutative algebra
AddCommGroupWithOne.natCast_zero
∀ {R : Type u} [self : AddCommGroupWithOne R], ↑0 = 0The canonical map ℕ → R sends 0 : ℕ to 0 : R.
- Defined in
- Mathlib.Data.Int.Cast.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- AddCommGroupWithOne
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.
- AddMonoid.toZerostatement · cited by 325
- AddCommGroupWithOnestatement and proof · cited by 61
- AddCommGroupWithOne.toNatCaststatement · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- AddCommGroupWithOne.extproof · cited by 2