Theorems · Theorem · group theory
mul_left_inj
∀ {G : Type u_1} [inst : Mul G] [IsRightCancelMul G] (a : G) {b c : G}, b * a = c * a ↔ b = c- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- MulIsRightCancelMul
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.
- IsRightCancelMulstatement and proof · cited by 43
- mul_left_injectiveproof · cited by 19
Cited by8
Results whose statement or proof uses this declaration.
- Subgroup.smul_diff'proof · cited by 2
- CategoryTheory.PresheafOfGroups.OneCohomologyRelation.symmproof · cited by 1
- Commute.of_orderOf_dvd_twoproof · cited by 1
- AddCircle.toCircle_negproof · cited by 1
- oneLePart_inf_leOnePart_eq_oneproof · cited by 0
- Finset.prod_eq_prod_iff_singleproof · cited by 0
- CategoryTheory.PresheafOfGroups.OneCocycle.ev_symmproof · cited by 0
- div_left_injproof · cited by 0