Theorems · Theorem · order theory
lt_of_tsub_lt_tsub_left_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 c : α} [AddLeftReflectLE α] [AddLeftReflectLT α], c ≤ a → a - b < a - c → c < bSee lt_of_tsub_lt_tsub_left for a stronger statement in a linear order.
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- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
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- 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
- AddLeftReflectLTstatement and proof · cited by 33
- AddLECancellable.lt_of_tsub_lt_tsub_left_of_leproof · cited by 2
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