Theorems · Theorem · order theory
mul_pos_iff_of_pos_left
∀ {α : Type u_1} [inst : MulZeroClass α] {a b : α} [inst_1 : Preorder α] [PosMulStrictMono α] [PosMulReflectLT α],
0 < a → (0 < a * b ↔ 0 < b)- Cited by
- 8 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- PosMulStrictMonostatement and proof · cited by 151
- mul_lt_mul_iff_right₀proof · cited by 14
Cited by8
Results whose statement or proof uses this declaration.
- RootPairing.RootPositiveForm.zero_lt_apply_root_root_iffproof · cited by 2
- Complex.stolzCone_subset_stolzSet_auxproof · cited by 1
- SimpleGraph.odd_card_odd_degree_vertices_neproof · cited by 1
- blimsup_thickening_mul_ae_eqproof · cited by 1
- Nat.Prime.sum_four_squaresproof · cited by 1
- Units.inv_posproof · cited by 0
- Matrix.diag_pos_of_mul_diagonal_posDefproof · cited by 0
- div_pos_iff_of_pos_leftproof · cited by 0