Theorems · Theorem · group theory
eq_mul_inv_of_mul_eq
∀ {G : Type u_3} [inst : Group G] {a b c : G}, a * c = b → a = b * c⁻¹- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- mul_oneproof · cited by 3,885
- mul_assocproof · cited by 1,667
- mul_inv_cancelproof · cited by 128
Cited by7
Results whose statement or proof uses this declaration.
- Subgroup.IsComplement.equiv_fst_eq_mul_invproof · cited by 8
- Set.mulIndicator_complproof · cited by 2
- pow_subproof · cited by 2
- Set.mulIndicator_sdiffproof · cited by 2
- DoubleCoset.mk_out_eq_mulproof · cited by 1
- DoubleCoset.iUnion_finset_leftRel_eq_univ_of_leftRelproof · cited by 0
- Subgroup.normalizer_singletonproof · cited by 0