Theorems · Theorem · order theory
tsub_lt_self
∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : LinearOrder α] [CanonicallyOrderedAdd α] [inst_3 : Sub α]
[OrderedSub α] {a b : α} [AddLeftReflectLE α], 0 < a → 0 < b → a - b < a- Defined in
- Mathlib.Algebra.Order.Sub.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
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
- LinearOrderstatement and proof · cited by 8,572
- OrderedSubstatement and proof · cited by 236
- CanonicallyOrderedAddstatement and proof · cited by 229
- AddLeftReflectLEstatement and proof · cited by 119
- Contravariant.AddLECancellableproof · cited by 45
- AddLECancellable.tsub_lt_selfproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_eraseLead_eq_nextCoeffproof · cited by 5
- Polynomial.natDegree_eraseLeadproof · cited by 2
- Nat.geomSum_ltproof · cited by 1
- Polynomial.natDegree_eraseLead_le_of_nextCoeff_eq_zeroproof · cited by 1
- blimsup_cthickening_ae_le_of_eventually_mul_le_auxproof · cited by 1
- norm_cfcₙ_one_sub_one_add_inv_lt_oneproof · cited by 1
- Nat.grahamConjecture_of_squarefreeproof · cited by 0