Theorems · Theorem · group theory
add_left_cancel_iff
∀ {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
- 17 results in Mathlib
- Foundations
- Depth 7 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
- add_left_cancelproof · cited by 29
Cited by17
Results whose statement or proof uses this declaration.
- add_eq_leftproof · cited by 37
- EuclideanDomain.mod_eq_zeroproof · cited by 5
- nsmul_eq_nsmul_iff_modEqproof · cited by 4
- Relation.cutExpand_add_leftproof · cited by 3
- Configuration.HasLines.lineCount_eq_pointCountproof · cited by 3
- AddLeftCancelMonoid.eq_zero_of_add_rightproof · cited by 3
- Ordinal.mul_eq_right_iff_opow_omega0_dvdproof · cited by 2
- AddLocalization.mk_eq_mk_iff'proof · cited by 1
- IsIdempotentElem.add_iffproof · cited by 1
- LieModule.toEnd_pow_lieproof · cited by 1
- AddSemiconjBy.addConj_iffproof · cited by 1
- LinearIsometry.im_apply_eq_im_or_neg_of_re_apply_eq_reproof · cited by 1