Theorems · Theorem · order theory
IsGLB.insert
∀ {γ : Type u_3} [inst : SemilatticeInf γ] (a : γ) {b : γ} {s : Set γ}, IsGLB s b → IsGLB (insert a s) (a ⊓ b)- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- SemilatticeInf
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
- SemilatticeInfstatement and proof · cited by 634
- IsGLBstatement and proof · cited by 213
- Set.insert_eqproof · cited by 47
- isGLB_singletonproof · cited by 7
- IsGLB.unionproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- isGLB_pairproof · cited by 5
- sInf_insertproof · cited by 4
- csInf_insertproof · cited by 0