Theorems · Theorem · order theory
sInf_union
∀ {α : Type u_1} [inst : CompleteLattice α] {s t : Set α}, sInf (s ∪ t) = sInf s ⊓ sInf t- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- CompleteLatticestatement and proof · cited by 1,048
- InfSet.sInfstatement · cited by 935
- isGLB_sInfproof · cited by 23
- IsGLB.sInf_eqproof · cited by 14
- IsGLB.unionproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Set.sInter_unionproof · cited by 4