Theorems · Theorem · order theory
mul_pos
∀ {α : Type u_1} [inst : MulZeroClass α] {a b : α} [inst_1 : Preorder α] [PosMulStrictMono α], 0 < a → 0 < b → 0 < a * bAlias of Left.mul_pos.
Assumes left covariance.
- Cited by
- 374 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 23 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement · cited by 7,952
- MulZeroClassstatement · cited by 232
- PosMulStrictMonostatement · cited by 151
- Left.mul_posproof · cited by 2
Cited by374
Results whose statement or proof uses this declaration.
- div_posproof · cited by 337
- Finset.prod_posproof · cited by 25
- Ordinal.opow_posproof · cited by 22
- mul_self_posproof · cited by 17
- Real.Gamma_pos_of_posproof · cited by 17
- Complex.arg_real_mulproof · cited by 11
- sq_pos_of_posproof · cited by 11
- mul_pos_iffproof · cited by 8
- Asymptotics.isLittleOTVS_iff_isLittleOproof · cited by 7
- summable_pow_mul_jacobiTheta₂_term_boundproof · cited by 6
- Complex.arg_mul_coe_angleproof · cited by 6
- HurwitzKernelBounds.summable_f_natproof · cited by 5
Showing the 200 most cited of 374.