Theorems · Theorem · order theory
mul_add_mul_lt_mul_add_mul
∀ {R : Type u} [inst : Semiring R] [inst_1 : PartialOrder R] {a b c d : R} [AddLeftReflectLT R] [ExistsAddOfLE R]
[MulPosStrictMono R] [AddLeftStrictMono R], a < b → c < d → a * d + b * c < a * c + b * dBinary strict rearrangement inequality.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- add_assocproof · cited by 746
- mul_addproof · cited by 413
- ExistsAddOfLEstatement and proof · cited by 330
- AddLeftStrictMonostatement and proof · cited by 203
- MulPosStrictMonostatement and proof · cited by 94
- add_right_commproof · cited by 85
- mul_lt_mul_of_pos_rightproof · cited by 54
- add_lt_add_rightproof · cited by 50
- AddLeftReflectLTstatement and proof · cited by 33
- exists_pos_add_of_lt'proof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- mul_add_mul_lt_mul_add_mul'proof · cited by 0