Theorems · Theorem · group theory
eq_of_sub_eq_zero
∀ {α : Type u_1} [inst : SubtractionMonoid α] {a b : α}, a - b = 0 → a = b- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- SubtractionMonoid
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.
- sub_eq_add_negproof · cited by 1,023
- SubtractionMonoidstatement and proof · cited by 208
- neg_injectiveproof · cited by 35
- neg_eq_of_add_eq_zero_rightproof · cited by 9
Cited by27
Results whose statement or proof uses this declaration.
- sub_eq_zeroproof · cited by 407
- sub_ne_zero_of_neproof · cited by 51
- Polynomial.div_modByMonic_uniqueproof · cited by 12
- Dioph.eq_diophproof · cited by 8
- minpoly.uniqueproof · cited by 7
- IsHausdorff.subsingletonproof · cited by 3
- Algebra.FinitePresentation.of_span_eq_top_targetproof · cited by 2
- HahnSeries.unit_auxproof · cited by 2
- IsIntegrallyClosed.minpoly.uniqueproof · cited by 2
- hasFDerivAt_of_tendstoUniformlyOnFilterproof · cited by 2
- Padic.const_equivproof · cited by 2
- LaurentSeries.eq_coeff_of_valuation_sub_ltproof · cited by 2