Theorems · Theorem · order theory
neg_lt_neg_iff
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddLeftStrictMono α] {a b : α} [AddRightStrictMono α],
-a < -b ↔ b < a- Cited by
- 39 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- zero_addproof · cited by 2,366
- add_neg_cancelproof · cited by 213
- AddLeftStrictMonostatement and proof · cited by 203
- AddRightStrictMonostatement and proof · cited by 160
- neg_add_cancel_rightproof · cited by 75
- add_lt_add_iff_rightproof · cited by 42
- add_lt_add_iff_leftproof · cited by 30
Cited by39
Results whose statement or proof uses this declaration.
- neg_ltproof · cited by 21
- neg_lt_negproof · cited by 20
- lt_negproof · cited by 12
- StrictAntiOn.negproof · cited by 4
- smul_lt_smul_iff_of_neg_leftproof · cited by 4
- lowerSemicontinuousWithinAt_neg_iffproof · cited by 4
- Complex.arg_le_pi_div_two_iffproof · cited by 4
- neg_strictConvexOn_iffproof · cited by 3
- monovary_neg_rightproof · cited by 3
- sub_lt_sub_iff_leftproof · cited by 3
- Real.summable_abs_int_rpowproof · cited by 3
- toIcoDiv_negproof · cited by 3