Theorems · Theorem · order theory
tsub_le_self
∀ {α : Type u_1} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [CanonicallyOrderedAdd α] [inst_3 : Sub α]
[OrderedSub α] {a b : α}, a - b ≤ a- Defined in
- Mathlib.Algebra.Order.Sub.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 8 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
- le_rflproof · cited by 1,558
- OrderedSubstatement and proof · cited by 236
- CanonicallyOrderedAddstatement and proof · cited by 229
- tsub_le_iff_leftproof · cited by 38
- le_add_leftproof · cited by 17
Cited by22
Results whose statement or proof uses this declaration.
- Polynomial.coeff_mirrorproof · cited by 4
- IsPrimitiveRoot.pow_injproof · cited by 4
- AddLECancellable.tsub_lt_selfproof · cited by 3
- catalan_eq_centralBinom_divproof · cited by 3
- ContinuousMap.idealOfSet_ofIdeal_eq_closureproof · cited by 2
- Polynomial.aeval_iterate_derivative_of_ltproof · cited by 2
- thickenedIndicatorAux_le_oneproof · cited by 2
- PairReduction.iSup_edist_pairSetproof · cited by 1
- tsub_lt_of_ltproof · cited by 1
- Nat.geom_sum_leproof · cited by 1
- Polynomial.exists_approx_polynomial_auxproof · cited by 1
- ProbabilityTheory.exists_integrable_exp_sq_of_map_rotation_eq_self'proof · cited by 1