Theorems · Theorem · order theory
neg_le_neg
∀ {α : Type u} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] {a b : α}, a ≤ b → -b ≤ -a- Defined in
- Mathlib.Algebra.Order.Group.Defs
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
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.
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- neg_le_neg_iffproof · cited by 57
Cited by34
Results whose statement or proof uses this declaration.
- Real.arcsin_negproof · cited by 11
- RealRMK.integral_rieszMeasureproof · cited by 7
- MeasureTheory.VectorMeasure.neg_le_negproof · cited by 6
- Real.le_arcsin_iff_sin_le'proof · cited by 4
- IsMinFilter.negproof · cited by 4
- IsMaxFilter.negproof · cited by 4
- existsUnique_zsmul_near_of_posproof · cited by 3
- ConcaveOn.le_slope_of_hasDerivWithinAt_Iioproof · cited by 3
- ConcaveOn.slope_le_of_hasDerivWithinAt_Ioiproof · cited by 3
- IsMaxOn.negproof · cited by 2
- ODE_solution_unique_of_mem_Icc_leftproof · cited by 2
- intervalIntegral.integral_le_sub_of_hasDeriv_right_of_leproof · cited by 2