Theorems · Theorem · order theory
add_tsub_cancel_right
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : AddCommSemigroup α] [inst_2 : Sub α] [OrderedSub α]
[AddLeftReflectLE α] (a b : α), a + b - b = a- Defined in
- Mathlib.Algebra.Order.Sub.Defs
- Cited by
- 172 results in Mathlib
- Foundations
- Depth 12 from the axioms, rests on 32 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.
- PartialOrderstatement and proof · cited by 6,410
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- AddLeftReflectLEstatement and proof · cited by 119
- Contravariant.AddLECancellableproof · cited by 45
- AddLECancellable.add_tsub_cancel_rightproof · cited by 9
Cited by172
Results whose statement or proof uses this declaration.
- Primrec.compproof · cited by 80
- Polynomial.coeff_derivativeproof · cited by 14
- Primrec.pairproof · cited by 9
- SimplexCategory.δ_comp_σ_selfproof · cited by 8
- PowerSeries.coeff_X_pow_mul'proof · cited by 7
- Nat.Primrec.predproof · cited by 7
- MvPowerSeries.monomial_mul_monomialproof · cited by 5
- Primrec.option_casesOnproof · cited by 5
- Polynomial.coeff_mul_X_pow'proof · cited by 5
- AlgebraicTopology.DoldKan.hσ'_eqproof · cited by 4
- Affine.Simplex.faceOppositeCentroid_vsub_point_eq_smul_sum_vsubproof · cited by 4
- MvPowerSeries.coeff_add_mul_monomialproof · cited by 4