Theorems · Theorem · order theory
sub_le_self
∀ {α : Type u} [inst : AddGroup α] [inst_1 : LE α] [AddLeftMono α] (a : α) {b : α}, 0 ≤ b → a - b ≤ aAlias of the reverse direction of sub_le_self_iff.
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- AddGroupLEAddLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddLeftMonostatement and proof · cited by 687
- sub_le_self_iffproof · cited by 7
Cited by14
Results whose statement or proof uses this declaration.
- Complex.arg_le_pi_div_two_iffproof · cited by 4
- MeasureTheory.hahn_decompositionproof · cited by 2
- Nat.cast_le_pow_div_subproof · cited by 1
- Complex.sum_div_factorial_leproof · cited by 1
- Convexity.continuous_convexCombPair_of_isBoundedproof · cited by 1
- IsCauSeq.geo_seriesproof · cited by 1
- ProbabilityTheory.variance_le_sq_of_boundedproof · cited by 1
- MeasureTheory.Submartingale.sum_sub_upcrossingStrat_mulproof · cited by 1
- ProbabilityTheory.Fernique.sq_normThreshold_add_one_leproof · cited by 1
- CFC.le_posPartproof · cited by 0
- Real.closedBall_eq_segmentproof · cited by 0
- monotoneOn_descPochhammer_evalproof · cited by 0