Theorems · Theorem · order theory
add_tsub_assoc_of_le
∀ {α : Type u_1} [inst : AddCommSemigroup α] [inst_1 : PartialOrder α] [ExistsAddOfLE α] [AddLeftMono α]
[inst_4 : Sub α] [OrderedSub α] {b c : α} [AddLeftReflectLE α], c ≤ b → ∀ (a : α), a + b - c = a + (b - c)See add_tsub_le_assoc for an inequality.
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- AddLeftMonostatement and proof · cited by 687
- ExistsAddOfLEstatement and proof · cited by 330
- 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_assoc_of_leproof · cited by 5
Cited by16
Results whose statement or proof uses this declaration.
- Finpartition.equitabilise_auxproof · cited by 3
- Configuration.Nondegenerate.exists_injective_of_card_leproof · cited by 2
- Affine.Simplex.mongePoint_eq_affineCombination_of_pointsWithCircumcenterproof · cited by 2
- wittPolynomial_zmod_selfproof · cited by 1
- Ideal.Filtration.submodule_eq_span_le_iff_stable_geproof · cited by 1
- Pell.xn_modEq_x2n_sub_lemproof · cited by 1
- Pell.xn_modEq_x4n_subproof · cited by 1
- Ideal.pow_multiset_sum_mem_span_powproof · cited by 1
- WittVector.map_frobeniusPoly.key₂proof · cited by 1
- Lagrange.interpolate_eq_sum_interpolate_insert_sdiffproof · cited by 1
- PadicInt.dvd_appr_sub_apprproof · cited by 1
- Finset.pluennecke_petridis_inequality_addproof · cited by 1