Theorems · Theorem · group theory
sub_ne_zero
∀ {G : Type u_3} [inst : AddGroup G] {a b : G}, a - b ≠ 0 ↔ a ≠ b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 119 results in Mathlib
- Foundations
- Depth 13 from the axioms, rests on 61 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 by119
Results whose statement or proof uses this declaration.
- meromorphicOrderAt_eq_int_iffproof · cited by 31
- meromorphicOrderAt_eq_top_iffproof · cited by 20
- meromorphicOrderAt_smulproof · cited by 10
- MeromorphicAt.invproof · cited by 9
- MeromorphicAt.meromorphicTrailingCoeffAt_smulproof · cited by 7
- ProbabilityTheory.aemeasurable_of_mem_interior_integrableExpSetproof · cited by 6
- Int.pairwise_one_le_distproof · cited by 5
- Real.abs_log_sub_add_sum_range_leproof · cited by 4
- Real.differentiableAt_binEntropyproof · cited by 4
- WeierstrassCurve.Jacobian.addZ_ne_zero_of_X_neproof · cited by 4
- orthonormal_fourierproof · cited by 3
- ProbabilityTheory.integrable_rpow_mul_exp_of_integrable_exp_mulproof · cited by 3