Mathlib Map

Theorems · Theorem · order theory

eq_of_mabs_div_eq_one

∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] {a b : G}, |a / b|ₘ = 1 → a = b
Defined in
Mathlib.Algebra.Order.Group.Abs
Cited by
1 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommGroupLinearOrderIsOrderedMonoid
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

eq_of_mabs_div_le_one · cited by 3eq_of_mabs_div_le_oneLinearOrder · cited by 8572LinearOrderCommGroup · cited by 990CommGroupIsOrderedMonoid · cited by 577IsOrderedMonoidmabs · cited by 148mabsdiv_eq_one · cited by 11div_eq_onemabs_eq_one · cited by 2mabs_eq_oneeq_of_mabs_div_eq_oneCITED BYCITES

Cites6

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.