Theorems · Theorem · order theory
inv_le_inv_iff
∀ {α : Type u} [inst : Group α] [inst_1 : LE α] [MulLeftMono α] {a b : α} [MulRightMono α], a⁻¹ ≤ b⁻¹ ↔ b ≤ a- Cited by
- 11 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.
- Groupstatement and proof · cited by 6,238
- one_mulproof · cited by 2,841
- MulLeftMonostatement and proof · cited by 410
- MulRightMonostatement and proof · cited by 263
- mul_inv_cancelproof · cited by 128
- inv_mul_cancel_rightproof · cited by 70
- mul_le_mul_iff_rightproof · cited by 19
- mul_le_mul_iff_leftproof · cited by 15
Cited by12
Results whose statement or proof uses this declaration.
- OrderIso.invproof · cited by 27
- inv_le_inv'proof · cited by 4
- min_inv_inv'proof · cited by 2
- max_inv_inv'proof · cited by 1
- leOnePart_antiproof · cited by 1
- mabs_le_max_mabs_mabsproof · cited by 1
- div_le_div_iff_leftproof · cited by 1
- Monotone.invproof · cited by 0
- Antitone.invproof · cited by 0
- MonotoneOn.invproof · cited by 0
- mabs_le_mabs_of_le_oneproof · cited by 0
- AntitoneOn.invproof · cited by 0