Theorems · Theorem · order theory
sSup_inv
∀ {M : Type u_1} [inst : CompleteLattice M] [inst_1 : Group M] [MulLeftMono M] [MulRightMono M] (s : Set M),
sSup s⁻¹ = (sInf s)⁻¹- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement and proof · cited by 954
- InfSet.sInfstatement and proof · cited by 935
- MulLeftMonostatement and proof · cited by 410
- MulRightMonostatement and proof · cited by 263
- Set.invstatement · cited by 132
- Set.image_inv_eq_invproof · cited by 44
- sSup_imageproof · cited by 36
- OrderIso.invproof · cited by 27
- OrderIso.map_sInfproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- sSup_divproof · cited by 0