Theorems · Theorem · order theory
Set.neg_mem_Icc_iff
∀ {α : Type u_1} [inst : AddCommGroup α] [inst_1 : PartialOrder α] [IsOrderedAddMonoid α] {a c d : α},
-a ∈ Set.Icc c d ↔ a ∈ Set.Icc (-d) (-c)- Defined in
- Mathlib.Algebra.Order.Interval.Set.Group
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 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.
- Setstatement · cited by 53,352
- AddCommGroupstatement and proof · cited by 12,871
- PartialOrderstatement and proof · cited by 6,410
- Set.Iccstatement · cited by 1,702
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- neg_leproof · cited by 27
- le_negproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- MonotoneOn.intervalIntegral_deriv_mem_uIccproof · cited by 0