Theorems · Theorem · order theory
lt_tsub_iff_left
∀ {α : Type u_1} {a b c : α} [inst : LinearOrder α] [inst_1 : AddCommSemigroup α] [inst_2 : Sub α] [OrderedSub α],
a < b - c ↔ c + a < bSee lt_tsub_iff_left_of_le for a weaker statement in a partial order.
- Defined in
- Mathlib.Algebra.Order.Sub.Defs
- Cited by
- 6 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- OrderedSubstatement and proof · cited by 236
- AddCommSemigroupstatement and proof · cited by 178
- lt_iff_lt_of_le_iff_leproof · cited by 54
- tsub_le_iff_leftproof · cited by 38
Cited by6
Results whose statement or proof uses this declaration.
- Metric.infEDist_le_infEDist_cthickening_addproof · cited by 3
- den_dvd_of_is_rootproof · cited by 2
- ENNReal.tendsto_subproof · cited by 2
- lt_tsub_commproof · cited by 1
- Finset.sum_range_diag_flipproof · cited by 1
- CompositionAsSet.blocksFun_posproof · cited by 0