Theorems · Theorem · group theory
sub_eq_zero_of_eq
∀ {G : Type u_3} [inst : AddGroup G] {a b : G}, a = b → a - b = 0Alias of the reverse direction of sub_eq_zero.
- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 154 results in Mathlib
- Foundations
- Depth 13 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.
Cites2
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_eq_zeroproof · cited by 407
Cited by154
Results whose statement or proof uses this declaration.
- Polynomial.div_modByMonic_uniqueproof · cited by 12
- Dioph.eq_diophproof · cited by 8
- Field.finSepDegree_eq_finrank_of_isSeparableproof · cited by 7
- intervalIntegral.intervalIntegrable_rpow'proof · cited by 6
- Real.rpowIntegrand₀₁_eq_pow_divproof · cited by 6
- Real.convexOn_log_Gammaproof · cited by 5
- Real.cos_pi_div_threeproof · cited by 5
- Real.log_lt_sub_one_of_posproof · cited by 4
- AbsoluteValue.isEquiv_iff_exists_rpow_eqproof · cited by 4
- AddCircle.injective_toCircleproof · cited by 4
- Real.tendsto_log_comp_add_sub_logproof · cited by 3
- padicNorm.int_eq_one_iffproof · cited by 3