Theorems · Theorem · order theory
sup_sub
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] [AddRightMono α] (a b c : α), a ⊔ b - c = (a - c) ⊔ (b - c)- Defined in
- Mathlib.Algebra.Order.Group.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- LatticeAddGroupAddRightMono
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.
- AddGroupstatement and proof · cited by 4,410
- Latticestatement and proof · cited by 916
- AddRightMonostatement and proof · cited by 367
- OrderIso.map_supproof · cited by 37
- OrderIso.subRightproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- sup_sub_inf_eq_abs_subproof · cited by 3