Theorems · Theorem · order theory
infClosure_min
∀ {α : Type u_3} [inst : SemilatticeInf α] {s t : Set α}, s ⊆ t → InfClosed t → infClosure s ⊆ t- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 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.
Cites7
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
- InfClosedstatement · cited by 57
- infClosurestatement · cited by 21
- ClosureOperator.closure_minproof · cited by 12
Cited by3
Results whose statement or proof uses this declaration.
- supClosure_infClosureproof · cited by 2
- infClosure_prodproof · cited by 1
- infClosure_supClosureproof · cited by 0