Theorems · Inductive type · order theory
AddRightReflectLE
(M : Type u_1) → [Add M] → [LE M] → Prop
Typeclass for reverse monotonicity of addition on the right,
namely a₁ + b ≤ a₂ + b → a₁ ≤ a₂.
You should usually not use this very granular typeclass directly, but rather a typeclass like
IsOrderedCancelAddMonoid.
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
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Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by56
Results whose statement or proof uses this declaration.
- add_le_add_iff_rightstatement and proof · cited by 47
- mul_nonneg_of_nonpos_of_nonposstatement and proof · cited by 45
- le_of_add_le_add_rightstatement and proof · cited by 15
- mul_le_mul_of_nonpos_rightstatement and proof · cited by 13
- le_add_iff_nonneg_leftstatement and proof · cited by 12
- mul_le_mul_of_nonpos_leftstatement and proof · cited by 11
- WithTop.le_of_add_le_add_rightstatement and proof · cited by 4
- antitone_mul_leftstatement and proof · cited by 3
- antitone_mul_rightstatement and proof · cited by 3
- WithTop.add_le_add_iff_rightstatement and proof · cited by 3
- AddRightReflectLE.le_of_add_le_add_rightstatement and proof · cited by 2
- add_le_iff_nonpos_leftstatement and proof · cited by 2