Theorems · Theorem · order theory
oneLePart_eq_one
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : DivInvMonoid α] {a : α}, a⁺ᵐ = 1 ↔ a ≤ 1- Defined in
- Mathlib.Algebra.Order.Group.PosPart
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext
- Assumes
- LatticeDivInvMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Latticestatement and proof · cited by 916
- DivInvMonoidstatement and proof · cited by 103
- sup_eq_rightproof · cited by 53
- OneLePart.oneLePartstatement · cited by 40
Cited by2
Results whose statement or proof uses this declaration.
- oneLePart_of_le_oneproof · cited by 0
- one_lt_oneLePart_iffproof · cited by 0