Theorems · Theorem · order theory
inf_eq_iInf
∀ {α : Type u_1} [inst : CompleteLattice α] (x y : α), x ⊓ y = ⨅ b, bif b then x else y- Defined in
- Mathlib.Order.CompleteLattice.Lemmas
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- iInf_bool_eqproof · cited by 4
Cited by19
Results whose statement or proof uses this declaration.
- Set.inter_eq_iInterproof · cited by 4
- Filter.lift'_infproof · cited by 1
- Ideal.mul_infproof · cited by 1
- continuousAdd_infproof · cited by 0
- completelyRegularSpace_infproof · cited by 0
- UniformFun.inf_eqproof · cited by 0
- RegularSpace.infproof · cited by 0
- isUniformAddGroup_infproof · cited by 0
- LocallyConvexSpace.infproof · cited by 0
- continuousInv_infproof · cited by 0
- topologicalAddGroup_infproof · cited by 0
- isUniformGroup_infproof · cited by 0