Structures · Data types
AddGroupWithOne
An AddGroupWithOne is an AddGroup with a 1. It also contains data for the unique
homomorphisms ℕ → R and ℤ → R.
- Defined in
- Mathlib.Data.Int.Cast.Defs
- Shape
- One type argument · adds sub_eq_add_neg, zsmul_zero', zsmul_succ', zsmul_neg', neg_add_cancel, intCast_ofNat, intCast_negSucc
Extends3
Extended by2
Concrete types that are instances19
- Complex
- Filter.Germ
- CStarMatrix
- Matrix
- TrivSqZeroExt
- DirectLimit
- Zsqrtd
- SkewMonoidAlgebra
- CauSeq
- LucasLehmer.X
- CommRingCat.Colimits.ColimitType
- Poly
- RingCat.Colimits.ColimitType
- Prod
- OrderDual
- ULift
- MulOpposite
- Lex
- Shrink
How is a type an instance?
Loading the hierarchy index…
Assumed by131
- Int.cast_natCast
- Int.cast_one
- Int.cast_neg
- Int.cast_zero
- Int.cast_add
- ZMod.cast
- Int.cast_ofNat
- Int.cast_sub
- Nat.cast_sub
- Int.cast_negSucc
- Int.cast_injective
- Nat.cast_natAbs
- zsmul_one
- Int.cast_inj
- Int.castAddHom
- Int.cast_ne_zero
- SimpleGraph.lapMatrix
- ArithmeticFunction.ofInt
- CharP.charP_to_charZero
- Nat.cast_card_eq_zero
- Nat.cast_pred
- CharP.intCast_eq_zero_iff
- Int.cast_eq_zero
- Int.cast_subNatNat
- AddGroupWithOne.toNeg
- ZNum.cast_to_int
- Int.cast_two
- AddGroupWithOne.toZSMul
- ZMod.cast_zero
- AddGroupWithOne.intCast_ofNat
- ZNum.cast_add
- PosNum.cast_to_int
- IsNonarchimedean.apply_intCast_le_one
- Num.cast_sub'
- Int.cast_negOfNat
- CharP.intCast_eq_intCast
- ZMod.cast_eq_val
- AddGroupWithOne.intCast_negSucc
- ArithmeticFunction.coe_coe
- AddGroupWithOne.toSub
- AddMonoidHom.eq_intCastAddHom
- AddConstMapClass.map_sub_int'
- ArithmeticFunction.intCoe_one
- PosNum.cast_sub'
- Matrix.map_intCast
- eq_intCast'
- AddGroupWithOne.sub_eq_add_neg
- map_intCast'
- Int.range_castAddHom
- Int.cast_eq_one
Ancestors37
- Add
- AddAction
- AddCancelMonoid
- AddGroup
- AddLeftCancelMonoid
- AddLeftCancelSemigroup
- AddMonoid
- AddMonoidWithOne
- AddRightCancelMonoid
- AddRightCancelSemigroup
- AddSemigroup
- AddSemigroupAction
- AddTorsor
- AddZero
- AddZeroClass
- HAdd
- HSub
- HVAdd
- IntCast
- InvolutiveNeg
- IsLeftCancelAdd
- IsRightCancelAdd
- NSMul
- NatCast
- Neg
- NegZeroClass
- Nonempty
- OfNat
- One
- Sub
- SubNegMonoid
- SubNegZeroMonoid
- SubtractionMonoid
- VAdd
- VSub
- ZSMul
- Zero