Theorems · Theorem · order theory
csInf_inv
∀ {M : Type u_1} [inst : ConditionallyCompleteLattice M] [inst_1 : Group M] [MulLeftMono M] [MulRightMono M]
{s : Set M}, s.Nonempty → BddAbove s → sInf s⁻¹ = (sSup s)⁻¹- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Set.Nonemptystatement and proof · cited by 2,627
- SupSet.sSupstatement and proof · cited by 954
- InfSet.sInfstatement and proof · cited by 935
- BddAbovestatement and proof · cited by 620
- MulLeftMonostatement and proof · cited by 410
- ConditionallyCompleteLatticestatement and proof · cited by 364
- MulRightMonostatement and proof · cited by 263
- Set.invstatement · cited by 132
- Set.image_inv_eq_invproof · cited by 44
- OrderIso.invproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- csInf_divproof · cited by 0