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Theorems · Theorem · commutative algebra

AddMonoidWithOne.natCast_zero

∀ {R : Type u_2} [self : AddMonoidWithOne R], ↑0 = 0

The canonical map ℕ → R sends 0 : ℕ to 0 : R.

Defined in
Mathlib.Data.Nat.Cast.Defs
Cited by
2 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
AddMonoidWithOne
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Nat.cast_zero · cited by 1870Nat.cast_zeroAddMonoidWithOne.ext · cited by 3AddMonoidWithOne.extFunction.Injective.nonAssocSemiring · cited by 0Injective.nonAssocSemiringFunction.Surjective.nonAssocSemiring · cited by 0Surjective.nonAssocSemiri…AddMonoid.toZero · cited by 325AddMonoid.toZeroAddMonoidWithOne · cited by 313AddMonoidWithOneAddMonoidWithOne.natCast_zeroCITED BYCITES

Cites2

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Cited by4

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