Theorems · Theorem · order theory
inv_mul_lt_iff_lt_mul
∀ {α : Type u} [inst : Group α] [inst_1 : LT α] [MulLeftStrictMono α] {a b c : α}, b⁻¹ * a < c ↔ a < b * c- Cited by
- 6 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- GroupLTMulLeftStrictMono
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
- MulLeftStrictMonostatement and proof · cited by 146
- mul_inv_cancel_leftproof · cited by 86
- mul_lt_mul_iff_leftproof · cited by 14
Cited by6
Results whose statement or proof uses this declaration.
- lt_mul_of_inv_mul_ltproof · cited by 1
- inv_mul_lt_iff_lt_mul'proof · cited by 1
- inv_mul_lt_of_lt_mulproof · cited by 0
- inv_mul_lt_one_iffproof · cited by 0
- inv_lt_div_iff_lt_mulproof · cited by 0
- mul_inv_lt_iff_le_mul'proof · cited by 0