Theorems · Theorem · order theory
le_tsub_iff_left
∀ {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], a ≤ c → (b ≤ c - a ↔ a + b ≤ c)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 11 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.le_tsub_iff_leftproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.integralNormalization_mul_C_leadingCoeffproof · cited by 2
- Configuration.Nondegenerate.exists_injective_of_card_leproof · cited by 2
- alternatingGroup.isConj_ofproof · cited by 1
- Polynomial.natDegree_eq_reverse_natDegree_add_natTrailingDegreeproof · cited by 1
- WittVector.map_frobeniusPoly.key₂proof · cited by 1