Theorems · Theorem · order theory
mul_inv_le_inv_mul_iff
∀ {α : Type u} [inst : Group α] [inst_1 : LE α] [MulLeftMono α] {a b c d : α} [MulRightMono α],
a * b⁻¹ ≤ d⁻¹ * c ↔ d * a ≤ c * b- Cited by
- 3 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
- mul_assocproof · cited by 1,667
- MulLeftMonostatement and proof · cited by 410
- MulRightMonostatement and proof · cited by 263
- mul_inv_cancel_leftproof · cited by 86
- inv_mul_cancel_rightproof · cited by 70
- mul_le_mul_iff_rightproof · cited by 19
- mul_le_mul_iff_leftproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- div_le_div''proof · cited by 8
- mul_inv_le_mul_inv_iff'proof · cited by 1
- div_le_inv_mul_iffproof · cited by 1