Theorems · Definition · order theory
absHom
{α : Type u_1} → [inst : Ring α] → [inst_1 : LinearOrder α] → [IsOrderedRing α] → α →*₀ αabs as a MonoidWithZeroHom.
- Defined in
- Mathlib.Algebra.Order.Ring.Abs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Quot.sound
- Assumes
- RingLinearOrderIsOrderedRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- absproof · cited by 1,814
- IsOrderedRingstatement and proof · cited by 777
- MonoidWithZeroHomstatement · cited by 704
- abs_mulproof · cited by 98
- abs_oneproof · cited by 87
Cited by5
Results whose statement or proof uses this declaration.
- abs_divproof · cited by 38
- abs_powproof · cited by 36
- abs_invproof · cited by 35
- Finset.abs_prodproof · cited by 9
- abs_zpowproof · cited by 1