Theorems · Theorem · order theory
isGLB_Ioi
∀ {γ : Type u_3} [inst : LinearOrder γ] [DenselyOrdered γ] {a : γ}, IsGLB (Set.Ioi a) a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- LinearOrderDenselyOrdered
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Set.Ioistatement and proof · cited by 1,463
- le_of_ltproof · cited by 1,175
- DenselyOrderedstatement and proof · cited by 471
- IsGLBstatement · cited by 213
- lowerBoundsproof · cited by 212
- le_of_forall_gt_imp_ge_of_denseproof · cited by 21
Cited by2
Results whose statement or proof uses this declaration.
- closure_Ioi'proof · cited by 5
- lowerBounds_Ioiproof · cited by 0