Mathlib Map

Theorems · Theorem · order theory

Right.one_le_inv_iff

∀ {α : Type u} [inst : Group α] [inst_1 : LE α] [MulRightMono α] {a : α}, 1 ≤ a⁻¹ ↔ a ≤ 1

Uses right co(ntra)variant.

Defined in
Mathlib.Algebra.Order.Group.Unbundled.Basic
Cited by
1 results in Mathlib
Foundations
Depth 14 from the axioms · uses propext
Assumes
GroupLEMulRightMono
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Right.self_le_inv · cited by 0Right.self_le_invGroup · cited by 6238Groupone_mul · cited by 2841one_mulMulRightMono · cited by 263MulRightMonoinv_mul_cancel · cited by 107inv_mul_cancelmul_le_mul_iff_right · cited by 19mul_le_mul_iff_rightRight.one_le_inv_iffCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.