Theorems · Theorem · order theory
subset_lowerBounds_mul
∀ {M : Type u_3} [inst : Mul M] [inst_1 : Preorder M] [MulLeftMono M] [MulRightMono M] (s t : Set M),
lowerBounds s * lowerBounds t ⊆ lowerBounds (s * t)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- MulLeftMonostatement and proof · cited by 410
- Set.mulstatement · cited by 297
- MulRightMonostatement and proof · cited by 263
- lowerBoundsstatement · cited by 212
- subset_upperBounds_mulproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- BddBelow.mulproof · cited by 0