Theorems · Theorem · order theory
GaloisConnection.u_csInf
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] [inst_1 : ConditionallyCompleteLattice β]
{l : α → β} {u : β → α}, GaloisConnection l u → ∀ {s : Set β}, s.Nonempty → BddBelow s → u (sInf s) = ⨅ x, u ↑x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
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Cites10
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.Elemstatement · cited by 7,166
- Set.Nonemptystatement and proof · cited by 2,627
- iInfstatement · cited by 1,690
- InfSet.sInfstatement · cited by 935
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- GaloisConnectionstatement and proof · cited by 253
- GaloisConnection.dualproof · cited by 4
- GaloisConnection.l_csSupproof · cited by 4
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