Theorems · Theorem · commutative algebra
AddGroupWithOne.intCast_negSucc
∀ {R : Type u} [self : AddGroupWithOne R] (n : ℕ), IntCast.intCast (Int.negSucc n) = -↑(n + 1)The canonical homomorphism ℤ → R for negative values is just the negation of the values
of the canonical homomorphism ℕ → R.
- Defined in
- Mathlib.Data.Int.Cast.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- AddGroupWithOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupWithOnestatement and proof · cited by 111
- AddGroupWithOne.toNegstatement · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Int.cast_negSuccproof · cited by 32
- AddGroupWithOne.extproof · cited by 2
- Function.Surjective.addCommGroupWithOneproof · cited by 0
- Function.Surjective.ringproof · cited by 0
- Function.Injective.ringproof · cited by 0
- Function.Injective.addCommGroupWithOneproof · cited by 0