Theorems · Theorem · order theory
eq_tsub_iff_add_eq_of_le
∀ {α : Type u_1} [inst : AddCommSemigroup α] [inst_1 : PartialOrder α] [ExistsAddOfLE α] [AddLeftMono α]
[inst_4 : Sub α] [OrderedSub α] {a b c : α} [AddLeftReflectLE α], c ≤ b → (a = b - c ↔ a + c = b)- Cited by
- 6 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.eq_tsub_iff_add_eq_of_leproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- Nat.floor_sub_natCastproof · cited by 3
- DirectSum.coe_mul_of_apply_of_leproof · cited by 2
- ProbabilityTheory.Kernel.setIntegral_densityproof · cited by 2
- DirectSum.coe_of_mul_apply_of_leproof · cited by 2
- ContinuousMultilinearMap.changeOrigin_toFormalMultilinearSeriesproof · cited by 1
- Configuration.ProjectivePlane.card_pointsproof · cited by 1