Theorems · Theorem · order theory
lt_neg
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LT α] [AddLeftStrictMono α] {a b : α} [AddRightStrictMono α],
a < -b ↔ b < -a- Cited by
- 12 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- neg_negproof · cited by 960
- AddLeftStrictMonostatement and proof · cited by 203
- AddRightStrictMonostatement and proof · cited by 160
- neg_lt_neg_iffproof · cited by 39
Cited by12
Results whose statement or proof uses this declaration.
- Set.neg_Ioiproof · cited by 6
- Real.log_intCast_nonnegproof · cited by 4
- lt_div_iff_of_negproof · cited by 3
- ODE_solution_unique_of_mem_Icc_leftproof · cited by 2
- Hyperreal.InfiniteNeg.negproof · cited by 2
- Pell.existsUnique_pos_generatorproof · cited by 1
- lt_neg_of_lt_negproof · cited by 1
- IsCauSeq.of_decreasing_boundedproof · cited by 1
- Pell.IsFundamental.zpow_ne_neg_zpowproof · cited by 1
- Set.neg_mem_Ioc_iffproof · cited by 0
- Set.neg_mem_Ioo_iffproof · cited by 0
- exists_lt_nsmul_of_negproof · cited by 0