Theorems · Theorem · order theory
isGLB_infClosure
∀ {α : Type u_3} [inst : SemilatticeInf α] {s : Set α} {a : α}, IsGLB (infClosure s) a ↔ IsGLB s a- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeInf
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- SemilatticeInfstatement and proof · cited by 634
- ClosureOperatorstatement · cited by 371
- IsGLBstatement · cited by 213
- lowerBoundsproof · cited by 212
- IsGreatestproof · cited by 112
- infClosurestatement · cited by 21
- lowerBounds_infClosureproof · cited by 1
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