Theorems · Theorem · order theory
add_mem_upperBounds_add
∀ {M : Type u_3} [inst : Add M] [inst_1 : Preorder M] [AddLeftMono M] [AddRightMono M] {s t : Set M} {a b : M},
a ∈ upperBounds s → b ∈ upperBounds t → a + b ∈ upperBounds (s + t)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Preorderstatement and proof · cited by 7,952
- AddLeftMonostatement and proof · cited by 687
- add_le_addproof · cited by 666
- AddRightMonostatement and proof · cited by 367
- Set.addstatement · cited by 338
- upperBoundsstatement and proof · cited by 263
- Set.forall_mem_image2proof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- subset_upperBounds_addproof · cited by 2
- add_mem_lowerBounds_addproof · cited by 0