Theorems · Theorem · group theory
sub_eq_zero
∀ {G : Type u_3} [inst : AddGroup G] {a b : G}, a - b = 0 ↔ a = b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 407 results in Mathlib
- Foundations
- Depth 12 from the axioms, rests on 58 definitions · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- sub_selfproof · cited by 996
- eq_of_sub_eq_zeroproof · cited by 27
Cited by407
Results whose statement or proof uses this declaration.
- sub_eq_zero_of_eqproof · cited by 154
- sub_ne_zeroproof · cited by 119
- smul_left_injectiveproof · cited by 25
- Submodule.comap_map_eqproof · cited by 23
- linearIndependent_iff'proof · cited by 22
- Int.cast_injproof · cited by 22
- ext_inner_rightproof · cited by 13
- ext_inner_leftproof · cited by 11
- Ideal.map_isPrime_of_surjectiveproof · cited by 11
- Polynomial.mem_nthRootsproof · cited by 9
- WeierstrassCurve.Projective.equation_iffproof · cited by 8
- Ideal.Quotient.mk_eq_mk_iff_sub_memproof · cited by 8
Showing the 200 most cited of 407.