Theorems · Theorem · order theory
sInf_mem_lowerBounds
∀ {α : Type u_1} [inst : CompleteSemilatticeInf α] {s : Set α}, sInf s ∈ lowerBounds s- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteSemilatticeInf
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
- InfSet.sInfstatement and proof · cited by 935
- lowerBoundsstatement · cited by 212
- reflproof · cited by 80
- isGLB_sInfproof · cited by 23
- CompleteSemilatticeInfstatement and proof · cited by 19
- le_isGLB_iffproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- lt_sInf_iffproof · cited by 1