Theorems · Definition · order theory
MulLeftReflectLT
(M : Type u_1) → [Mul M] → [LT M] → Prop
Typeclass for strict reverse monotonicity of multiplication on the left,
namely a * b₁ < a * b₂ → b₁ < b₂.
You should usually not use this very granular typeclass directly, but rather a typeclass like
IsOrderedMonoid.
- Cited by
- 16 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.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ContravariantClassproof · cited by 15
Cited by16
Results whose statement or proof uses this declaration.
- mul_lt_mul_iff_leftstatement and proof · cited by 14
- lt_of_mul_lt_mul_left'statement and proof · cited by 5
- le_of_forall_one_lt_le_mulstatement and proof · cited by 3
- one_lt_of_lt_mul_rightstatement and proof · cited by 3
- exists_one_lt_mul_of_lt'statement and proof · cited by 1
- le_of_forall_one_lt_lt_mul'statement and proof · cited by 1
- le_iff_forall_one_lt_le_mulstatement and proof · cited by 1
- mul_lt_iff_lt_one_left'statement and proof · cited by 0
- OrderedCommGroup.lt_of_mul_lt_mul_leftstatement · cited by 0
- mulLeftReflectLT_of_mulLeftMonostatement · cited by 0
- lt_mul_iff_one_lt_right'statement and proof · cited by 0
- lt_iff_exists_one_lt_mulstatement and proof · cited by 0