Theorems · Theorem · order theory
isGLB_sInf
∀ {α : Type u_1} [inst : CompleteSemilatticeInf α] (s : Set α), IsGLB s (sInf s)- Defined in
- Mathlib.Order.CompleteLattice.Defs
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- CompleteSemilatticeInf
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.
- Setstatement and proof · cited by 53,352
- InfSet.sInfstatement · cited by 935
- IsGLBstatement · cited by 213
- CompleteSemilatticeInfstatement and proof · cited by 19
- CompleteSemilatticeInf.isGLB_sInfproof · cited by 1
Cited by24
Results whose statement or proof uses this declaration.
- sInf_leproof · cited by 110
- le_sInfproof · cited by 51
- GaloisConnection.u_iInfproof · cited by 40
- sInf_le_sInfproof · cited by 23
- le_sInf_iffproof · cited by 13
- isGLB_iInfproof · cited by 7
- sInf_lt_iffproof · cited by 7
- sInf_image2_eq_sInf_sInfproof · cited by 5
- sInf_insertproof · cited by 4
- sInf_upperBounds_eq_sSupproof · cited by 2
- RightOrdContinuous.map_sInf'proof · cited by 2
- sInf_le_sInf_of_isCoinitialForproof · cited by 2