Theorems · Theorem · order theory
le_add_self
∀ {α : Type u} [inst : Add α] [inst_1 : LE α] [CanonicallyOrderedAdd α] {a b : α}, a ≤ b + a- Cited by
- 51 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- AddLECanonicallyOrderedAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CanonicallyOrderedAddstatement and proof · cited by 229
- CanonicallyOrderedAdd.le_add_selfproof · cited by 1
Cited by51
Results whose statement or proof uses this declaration.
- self_le_add_leftproof · cited by 18
- Ordinal.opow_addproof · cited by 9
- Matroid.eRk_union_le_eRk_add_eRkproof · cited by 6
- le_of_add_le_rightproof · cited by 5
- Ordinal.sub_le_selfproof · cited by 4
- AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInftyproof · cited by 4
- AddLECancellable.tsub_le_tsub_iff_leftproof · cited by 4
- ContMDiffWithinAt.mlieBracketWithin_vectorFieldproof · cited by 3
- Ordinal.natCast_add_omega0proof · cited by 3
- Metric.ediam_union_le_add_edistproof · cited by 3
- le_add_of_le_rightproof · cited by 3
- MvPowerSeries.coeff_mul_left_one_sub_of_lt_weightedOrderproof · cited by 2