Theorems · Theorem · order theory
tsub_self
∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [CanonicallyOrderedAdd α] [inst_3 : Sub α]
[OrderedSub α] (a : α), a - a = 0- Defined in
- Mathlib.Algebra.Order.Sub.Basic
- Cited by
- 154 results in Mathlib
- Foundations
- Depth 11 from the axioms, rests on 52 definitions · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- le_rflproof · cited by 1,558
- OrderedSubstatement and proof · cited by 236
- CanonicallyOrderedAddstatement and proof · cited by 229
- tsub_eq_zero_of_leproof · cited by 26
Cited by154
Results whose statement or proof uses this declaration.
- Polynomial.derivative_Xproof · cited by 34
- Nat.totient_primeproof · cited by 11
- Derivation.leibniz_powproof · cited by 10
- wittPolynomial_zeroproof · cited by 8
- Nat.factorization_divproof · cited by 7
- MeasureTheory.Measure.sub_applyproof · cited by 5
- Polynomial.natDegree_divByMonicproof · cited by 5
- Polynomial.coeffList_eraseLeadproof · cited by 4
- Polynomial.coeff_scaleRoots_natDegreeproof · cited by 4
- Nat.not_dvd_ordComplproof · cited by 4
- Subgroup.nilpotent_iff_finite_descending_central_seriesproof · cited by 4
- ProbabilityTheory.Kernel.singularPart_compl_mutuallySingularSetSliceproof · cited by 4