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Theorems · Theorem · commutative algebra

AddMonoidWithOne.natCast_succ

∀ {R : Type u_2} [self : AddMonoidWithOne R] (n : ℕ), ↑(n + 1) = ↑n + 1

The canonical map ℕ → R is a homomorphism.

Defined in
Mathlib.Data.Nat.Cast.Defs
Cited by
2 results in Mathlib
Foundations
Depth 8 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_succ · cited by 99Nat.cast_succAddMonoidWithOne.ext · cited by 3AddMonoidWithOne.extFunction.Injective.nonAssocSemiring · cited by 0Injective.nonAssocSemiringFunction.Surjective.nonAssocSemiring · cited by 0Surjective.nonAssocSemiri…AddMonoidWithOne · cited by 313AddMonoidWithOneAddMonoidWithOne.natCast_succCITED BYCITES

Cites1

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Cited by4

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