Theorems · Theorem · order theory
le_inv_mul_iff_mul_le
∀ {α : Type u} [inst : Group α] [inst_1 : LE α] [MulLeftMono α] {a b c : α}, b ≤ a⁻¹ * c ↔ a * b ≤ c- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- GroupLEMulLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- MulLeftMonostatement and proof · cited by 410
- mul_inv_cancel_leftproof · cited by 86
- mul_le_mul_iff_leftproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- mul_le_of_le_inv_mulproof · cited by 0
- le_inv_mul_of_mul_leproof · cited by 0