Theorems · Theorem · order theory
sInf_insert
∀ {α : Type u_1} [inst : CompleteLattice α] {a : α} {s : Set α}, sInf (insert a s) = a ⊓ sInf s- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 4 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.insertproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Set.sInter_insertproof · cited by 8
- sInf_le_sInf_of_subset_insert_topproof · cited by 4
- Ideal.comap_jacobson_of_surjectiveproof · cited by 2
- Submodule.CoFG.sInfproof · cited by 1