Theorems · Theorem · order theory
tsub_pos_iff_lt
∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : LinearOrder α] [CanonicallyOrderedAdd α] [inst_3 : Sub α]
[OrderedSub α] {a b : α}, 0 < a - b ↔ b < a- Defined in
- Mathlib.Algebra.Order.Sub.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- LinearOrderstatement and proof · cited by 8,572
- not_leproof · cited by 328
- OrderedSubstatement and proof · cited by 236
- CanonicallyOrderedAddstatement and proof · cited by 229
- tsub_pos_iff_not_leproof · cited by 2
Cited by27
Results whose statement or proof uses this declaration.
- ENNReal.tsum_geometricproof · cited by 8
- IsPrimitiveRoot.norm_pow_sub_one_of_prime_pow_ne_twoproof · cited by 4
- Nat.geomSum_eqproof · cited by 3
- ENNReal.lt_iff_exists_add_pos_ltproof · cited by 3
- AddLECancellable.tsub_lt_selfproof · cited by 3
- Nat.fib_lt_fib_succproof · cited by 2
- cauchySeq_of_edist_le_geometricproof · cited by 2
- Metric.eventually_nhds_zero_forall_closedEBall_subsetproof · cited by 2
- IsCyclic.normalizer_le_centralizerproof · cited by 2
- AntilipschitzWith.add_lipschitzWithproof · cited by 2
- AddRightCancelMonoid.finite_multiplesproof · cited by 1
- NNReal.sqrt_mul_lt_half_add_of_neproof · cited by 1