Theorems · Theorem · order theory
CanonicallyOrderedAdd.toIsOrderedAddMonoid
∀ {α : Type u} [inst : AddCommMonoid α] [inst_1 : Preorder α] [CanonicallyOrderedAdd α], IsOrderedAddMonoid α- Cited by
- 5 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Preorderstatement and proof · cited by 7,952
- IsOrderedAddMonoidstatement · cited by 1,659
- CanonicallyOrderedAddstatement and proof · cited by 229
- add_le_add_leftproof · cited by 37
Cited by5
Results whose statement or proof uses this declaration.
- Finset.sum_le_sum_of_subsetproof · cited by 14
- Finset.sum_mono_setproof · cited by 6
- Finset.sum_le_sum_of_ne_zeroproof · cited by 2
- Finset.single_le_sum_of_canonicallyOrderedproof · cited by 2
- Finset.sum_pos_iffproof · cited by 0