Theorems · Theorem · group theory
add_left_cancel
∀ {G : Type u_1} [inst : Add G] [IsLeftCancelAdd G] {a b c : G}, a + b = a + c → b = c- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- AddIsLeftCancelAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsLeftCancelAddstatement and proof · cited by 72
- IsLeftCancelAdd.add_left_cancelproof · cited by 1
Cited by29
Results whose statement or proof uses this declaration.
- add_right_injectiveproof · cited by 36
- add_left_cancel_iffproof · cited by 17
- Function.Injective.isLeftCancelAddproof · cited by 3
- Ideal.IsHomogeneous.isPrime_of_homogeneous_mem_or_memproof · cited by 3
- AddSubgroup.isComplement_singleton_univproof · cited by 3
- MeasureTheory.FinMeasAdditive.map_empty_eq_zeroproof · cited by 3
- LinearMap.IsAlt.eq_of_add_add_eq_zeroproof · cited by 2
- Differential.algHom_derivproof · cited by 2
- ComplexShape.hasNoLoop_up'proof · cited by 2
- Set.AddAntidiagonal.fst_eq_fst_iff_snd_eq_sndproof · cited by 2
- Affine.Simplex.finrank_direction_altitudeproof · cited by 1
- AddCommMagma.IsLeftCancelAdd.toIsRightCancelAddproof · cited by 1