Theorems · Theorem · order theory
tsub_eq_zero_of_le
∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [CanonicallyOrderedAdd α] [inst_3 : Sub α]
[OrderedSub α] {a b : α}, a ≤ b → a - b = 0Alias of the reverse direction of tsub_eq_zero_iff_le.
- Defined in
- Mathlib.Algebra.Order.Sub.Basic
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- PartialOrderstatement and proof · cited by 6,410
- OrderedSubstatement and proof · cited by 236
- CanonicallyOrderedAddstatement and proof · cited by 229
- tsub_eq_zero_iff_leproof · cited by 32
Cited by26
Results whose statement or proof uses this declaration.
- tsub_selfproof · cited by 154
- zero_tsubproof · cited by 100
- ENNReal.sub_mulproof · cited by 8
- Nat.factorization_divproof · cited by 7
- ENNReal.ofReal_subproof · cited by 5
- Nat.cast_tsubproof · cited by 4
- Subgroup.is_descending_rev_series_of_is_ascendingproof · cited by 3
- infEDist_thickeningproof · cited by 3
- MeasureTheory.exists_isSigmaFiniteSet_measure_geproof · cited by 3
- thickenedIndicatorAux_mono_infEDistproof · cited by 3
- ENNReal.continuous_sub_rightproof · cited by 2
- MeasureTheory.le_addContent_sdiffproof · cited by 2