Theorems · Theorem · order theory
pos_of_mul_pos_right
∀ {α : Type u_1} [inst : MulZeroClass α] {a b : α} [inst_1 : Preorder α] [PosMulReflectLT α], 0 < a * b → 0 ≤ a → 0 < b- Cited by
- 6 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- MulZeroClass.mul_zeroproof · cited by 2,091
- PosMulReflectLTstatement and proof · cited by 278
- MulZeroClassstatement and proof · cited by 232
- lt_of_mul_lt_mul_leftproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- invOf_posproof · cited by 3
- invOf_nonnegproof · cited by 2
- ContinuousLinearEquiv.norm_symm_posproof · cited by 2
- SzemerediRegularity.eps_pow_five_posproof · cited by 2
- one_mem_posTangentConeAt_iff_mem_closureproof · cited by 1
- pos_iff_pos_of_mul_posproof · cited by 0