Theorems · Theorem · order theory
lowerBounds_Ioi
∀ {γ : Type u_3} [inst : LinearOrder γ] [DenselyOrdered γ] {a : γ}, lowerBounds (Set.Ioi a) = Set.Iic a- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrderDenselyOrdered
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.Ioistatement · cited by 1,463
- Set.Iicstatement · cited by 1,111
- DenselyOrderedstatement and proof · cited by 471
- lowerBoundsstatement · cited by 212
- IsGLB.lowerBounds_eqproof · cited by 11
- isGLB_Ioiproof · cited by 2
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