Theorems · Theorem · order theory
sup_lt_iff
∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, max b c < a ↔ b < a ∧ c < a- Defined in
- Mathlib.Order.Lattice
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- LE.le.trans_ltproof · cited by 795
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- sup_indproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- max_lt_iffproof · cited by 22
- PowerSeries.IsWeierstrassDivisionAt.addproof · cited by 2
- Rat.AbsoluteValue.eq_one_of_not_dvdproof · cited by 1
- negPart_ltproof · cited by 0
- oneLePart_ltproof · cited by 0
- Set.Ioi_inter_Ioiproof · cited by 0
- posPart_ltproof · cited by 0
- CauSeq.sup_limZeroproof · cited by 0
- leOnePart_ltproof · cited by 0