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Theorems · Theorem · order theory

div_le_inv_mul_iff

∀ {α : Type u} [inst : Group α] [inst_1 : LinearOrder α] [MulLeftMono α] {a b : α} [MulRightMono α],
  a / b ≤ a⁻¹ * b ↔ a ≤ b
Defined in
Mathlib.Algebra.Order.Group.Unbundled.Basic
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext
Assumes
GroupLinearOrderMulLeftMonoMulRightMono
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

div_le_div_flip · cited by 0div_le_div_flipLinearOrder · cited by 8572LinearOrderGroup · cited by 6238Groupdiv_eq_mul_inv · cited by 715div_eq_mul_invMulLeftMono · cited by 410MulLeftMononot_lt · cited by 306not_ltmul_le_mul' · cited by 274mul_le_mul'MulRightMono · cited by 263MulRightMonomul_lt_mul_of_lt_of_lt · cited by 9mul_lt_mul_of_lt_of_ltmul_inv_le_inv_mul_iff · cited by 3mul_inv_le_inv_mul_iffdiv_le_inv_mul_iffCITED BYCITES

Cites9

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Cited by1

Results whose statement or proof uses this declaration.