Theorems · Theorem · order theory
tsub_le_tsub
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : AddCommSemigroup α] [inst_2 : Sub α] [OrderedSub α] {a b c d : α}
[AddLeftMono α], a ≤ b → c ≤ d → a - d ≤ b - c- Defined in
- Mathlib.Algebra.Order.Sub.Defs
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.transproof · cited by 3,151
- AddLeftMonostatement and proof · cited by 687
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- tsub_le_tsub_rightproof · cited by 16
- tsub_le_tsub_leftproof · cited by 15
Cited by18
Results whose statement or proof uses this declaration.
- thickenedIndicatorAux_zeroproof · cited by 4
- HasFPowerSeriesWithinOnBall.changeOriginproof · cited by 3
- Int.erdos_ginzburg_zivproof · cited by 2
- antitone_const_tsubproof · cited by 2
- thickenedIndicatorAux_monoproof · cited by 2
- BoxIntegral.hasIntegralIndicatorConstproof · cited by 1
- MeasureTheory.lintegral_iInf_aeproof · cited by 1
- NNReal.dist_gm_am_leproof · cited by 1
- ProbabilityTheory.Fernique.lintegral_exp_mul_sq_norm_le_mulproof · cited by 1
- ProbabilityTheory.Fernique.logRatio_monoproof · cited by 1
- Finset.pluennecke_petridis_inequality_addproof · cited by 1