Theorems · Theorem · order theory
lt_min
∀ {α : Type u_1} [inst : LinearOrder α] {a b c : α}, a < b → a < c → a < min b c- Defined in
- Mathlib.Order.Defs.LinearOrder
- Cited by
- 69 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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_totalproof · cited by 294
- min_eq_leftproof · cited by 67
- min_eq_rightproof · cited by 54
Cited by69
Results whose statement or proof uses this declaration.
- HasFPowerSeriesAt.congrproof · cited by 6
- nhdsGE_basis_of_exists_gtproof · cited by 6
- IsOpen.analyticOn_iff_analyticOnNhdproof · cited by 5
- UniformSpace.hasBasis_ofFunproof · cited by 3
- intervalIntegral.integrableOn_Ioo_rpow_iffproof · cited by 3
- TFAE_mem_nhdsGEproof · cited by 3
- ConvexOn.hasDerivWithinAt_sInf_slope_of_mem_interiorproof · cited by 2
- FormalMultilinearSeries.comp_summable_nnrealproof · cited by 2
- BoxIntegral.Prepartition.injOn_setOfPred_mem_Icc_setOfPred_lower_eqproof · cited by 2
- Metric.AreSeparated.union_leftproof · cited by 2
- ENNReal.hasBasis_nhds_of_ne_top'proof · cited by 2
- IsClosed.Icc_subset_of_forall_mem_nhdsGT_of_Icc_subsetproof · cited by 2