Theorems · Theorem · order theory
lt_inf_iff
∀ {α : Type u} [inst : LinearOrder α] {a b c : α}, a < min b c ↔ a < b ∧ a < c- Defined in
- Mathlib.Order.Lattice
- Cited by
- 7 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
- inf_le_leftproof · cited by 286
- inf_le_rightproof · cited by 238
- LE.le.trans_lt'proof · cited by 50
- inf_indproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- lt_min_iffproof · cited by 14
- Set.Iio_inter_Iioproof · cited by 2
- Finset.lt_inf_iffproof · cited by 2
- AnalyticAt.eventually_constant_or_nhds_le_map_nhds_auxproof · cited by 1
- CauSeq.sup_ltproof · cited by 1
- CauSeq.lt_infproof · cited by 1
- CauSeq.inf_limZeroproof · cited by 0