Theorems · Definition · order theory
AddRightReflectLT
(M : Type u_1) → [Add M] → [LT M] → Prop
Typeclass for strict 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
IsOrderedAddMonoid.
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
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.
- Function.swapproof · cited by 216
- ContravariantClassproof · cited by 15
Cited by29
Results whose statement or proof uses this declaration.
- add_lt_add_iff_rightstatement and proof · cited by 42
- mul_pos_of_neg_of_negstatement and proof · cited by 40
- lt_of_add_lt_add_rightstatement and proof · cited by 11
- lt_add_iff_pos_leftstatement and proof · cited by 8
- mul_lt_mul_of_neg_rightstatement and proof · cited by 6
- mul_lt_mul_of_neg_leftstatement and proof · cited by 5
- strictAnti_mul_leftstatement and proof · cited by 5
- strictAnti_mul_rightstatement and proof · cited by 5
- WithBot.add_lt_add_iff_rightstatement and proof · cited by 3
- WithTop.add_lt_add_iff_rightstatement and proof · cited by 2
- add_lt_iff_neg_rightstatement and proof · cited by 1
- mul_lt_mul_left_of_negstatement and proof · cited by 1