Theorems · Theorem · order theory
neg_lt_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
- 20 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, 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_lt_neg_iffproof · cited by 39
Cited by20
Results whose statement or proof uses this declaration.
- Real.sigmoid_strictMonoproof · cited by 5
- Real.abs_log_sub_add_sum_range_leproof · cited by 4
- HasDerivAt.lhopital_zero_left_on_Iooproof · cited by 3
- StrictConcaveOn.lt_slope_of_hasDerivWithinAt_Iioproof · cited by 2
- Complex.norm_prime_cpow_le_one_halfproof · cited by 2
- ConvexOn.strictAntiOnproof · cited by 2
- EReal.neg_strictAntiproof · cited by 2
- strictMono_of_odd_strictMonoOn_nonnegproof · cited by 2
- UpperHalfPlane.IsZeroAtImInfty.petersson_exp_decay_leftproof · cited by 2
- StrictConcaveOn.lt_slope_of_hasDerivWithinAtproof · cited by 1
- StrictConcaveOn.slope_lt_of_hasDerivAtproof · cited by 1
- StrictConcaveOn.slope_lt_of_hasDerivWithinAtproof · cited by 1