Theorems · Theorem · order theory
lt_imp_lt_of_le_of_le
∀ {α : Type u_2} [inst : Preorder α] {a b c d : α}, c ≤ a → b ≤ d → a < b → c < dmonotonicity of < with respect to →
- Defined in
- Mathlib.Order.Basic
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- LE.le.trans_ltproof · cited by 795
- LT.lt.trans_leproof · cited by 678
Cited by53
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_mul_leproof · cited by 10
- Complex.canonicalFactor_ne_zeroproof · cited by 6
- Ideal.ramificationIdx_posproof · cited by 5
- IsIntegral.coeffproof · cited by 4
- TendstoLocallyUniformlyOn.smul₀_of_isBoundedUnderproof · cited by 4
- MeasureTheory.MemLp.of_measure_le_smulproof · cited by 3
- MeasureTheory.Measure.IsEverywherePos.of_forall_exists_nhds_eqproof · cited by 3
- Cardinal.mk_Ioi_realproof · cited by 3
- Stirling.log_stirlingSeq_sdiff_leproof · cited by 3
- BoundedVariationOn.bilinear_compproof · cited by 3
- Polynomial.Sequence.span_degreeLTproof · cited by 3
- round_eq_divproof · cited by 2