Theorems · Theorem · group theory
Units.ext
∀ {α : Type u} [inst : Monoid α] {u v : αˣ}, ↑u = ↑v → u = v- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 86 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- Units.val_injectiveproof · cited by 17
Cited by86
Results whose statement or proof uses this declaration.
- Units.ext_iffproof · cited by 29
- Units.mk0_valproof · cited by 19
- Matrix.SpecialLinearGroup.coeToGL_detproof · cited by 10
- ZMod.unitsMap_surjectiveproof · cited by 7
- IsUnit.unit_oneproof · cited by 6
- CommRing.Pic.mk_eq_iffproof · cited by 5
- ModularGroup.SL_neg_smulproof · cited by 5
- IsUnit.unit_of_val_unitsproof · cited by 5
- Units.map_idproof · cited by 4
- Units.map_injectiveproof · cited by 4
- Units.mk0_oneproof · cited by 4
- Matrix.SpecialLinearGroup.map_mapGLproof · cited by 3