Theorems · Theorem · order theory
sub_inv_antitoneOn_Iio
∀ {α : Type u_2} [inst : Field α] [inst_1 : PartialOrder α] [PosMulReflectLT α] [IsStrictOrderedRing α] {c : α},
AntitoneOn (fun x => (x - c)⁻¹) (Set.Iio c)- Defined in
- Mathlib.Algebra.Order.Field.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- le_rflproof · cited by 1,558
- le_of_ltproof · cited by 1,175
- Set.Iiostatement and proof · cited by 1,166
- PosMulReflectLTstatement and proof · cited by 278
- AntitoneOnstatement · cited by 266
- sub_le_subproof · cited by 24
- sub_negproof · cited by 22
- antitoneOn_iff_forall_ltproof · cited by 6
- inv_le_inv_of_negproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- sub_inv_antitoneOn_Icc_leftproof · cited by 1
- inv_antitoneOn_Iioproof · cited by 0