Theorems · Theorem · order theory
isGLB_csInf
∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {s : Set α},
s.Nonempty → autoParam (BddBelow s) isGLB_csInf._auto_1 → IsGLB s (sInf s)- Cited by
- 24 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- ConditionallyCompleteLattice
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
- Set.Nonemptystatement and proof · cited by 2,627
- InfSet.sInfstatement · cited by 935
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- IsGLBstatement · cited by 213
- ConditionallyCompleteLattice.isGLB_csInfproof · cited by 1
Cited by24
Results whose statement or proof uses this declaration.
- csInf_leproof · cited by 51
- le_csInfproof · cited by 36
- IsGLB.csInf_eqproof · cited by 13
- csInf_image2_eq_csInf_csInfproof · cited by 5
- csInf_lt_iffproof · cited by 4
- IsClosed.csInf_memproof · cited by 3
- isGLB_ciInfproof · cited by 3
- le_csInf_iffproof · cited by 3
- IsCompact.isGLB_sInfproof · cited by 3
- IsClosed.isLeast_csInfproof · cited by 3
- csInf_le_csSupproof · cited by 2
- upperClosure_eq_Ici_csInfproof · cited by 2