Theorems · Theorem · order theory
tsub_tsub_cancel_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 : α} [AddLeftReflectLE α], a ≤ b → b - (b - a) = aSee tsub_tsub_le for an inequality.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 12 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.tsub_tsub_cancel_of_leproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- alternatingGroup.isMultiplyPretransitiveproof · cited by 4
- Polynomial.bernoulli_defproof · cited by 4
- Algebra.trace_eq_zero_of_not_isSeparableproof · cited by 2
- Finset.prod_Ico_reflectproof · cited by 2
- Polynomial.isNilpotent_reflect_iffproof · cited by 2
- Polynomial.aeval_iterate_derivative_selfproof · cited by 1
- Pell.eq_of_xn_modEq'proof · cited by 1
- Polynomial.exists_approx_polynomial_auxproof · cited by 1
- Pell.xn_modEq_x2n_subproof · cited by 1
- tsub_tsub_eq_minproof · cited by 0