Theorems · Theorem · order theory
tsub_eq_zero_iff_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 = 0 ↔ a ≤ b- Defined in
- Mathlib.Algebra.Order.Sub.Basic
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- add_zeroproof · cited by 2,707
- OrderedSubstatement and proof · cited by 236
- CanonicallyOrderedAddstatement and proof · cited by 229
- nonpos_iff_eq_zeroproof · cited by 100
- tsub_le_iff_leftproof · cited by 38
Cited by32
Results whose statement or proof uses this declaration.
- tsub_eq_zero_of_leproof · cited by 26
- Finset.sum_Ico_eq_sum_rangeproof · cited by 10
- ENNReal.tsum_geometricproof · cited by 8
- exists_prime_orderOf_dvd_cardproof · cited by 5
- Polynomial.natDegree_divByMonicproof · cited by 5
- IsPrimitiveRoot.pow_injproof · cited by 4
- PNat.sub_coeproof · cited by 3
- Subgroup.is_ascending_rev_series_of_is_descendingproof · cited by 3
- Nat.ceil_sub_natCastproof · cited by 3
- Nat.floor_sub_natCastproof · cited by 3
- MeasureTheory.prob_compl_eq_zero_iff₀proof · cited by 2
- AddSubgroup.is_ascending_rev_series_of_is_descendingproof · cited by 2