Theorems · Theorem · functional analysis
Unitization.inr_nonneg_iff
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {a : A}, 0 ≤ ↑a ↔ 0 ≤ a- Cited by
- 8 results in Mathlib
- Foundations
- Depth 318 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointproof · cited by 545
- Unitizationstatement · cited by 220
- NonUnitalCStarAlgebrastatement and proof · cited by 149
- Unitization.inrstatement and proof · cited by 109
- IsSelfAdjoint.of_nonnegproof · cited by 43
- Unitization.inr_le_iffproof · cited by 8
- Unitization.isSelfAdjoint_inrproof · cited by 5
- Unitization.inr_zeroproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- CFC.monotoneOn_one_sub_one_add_invproof · cited by 2
- Unitization.LE.le.inrproof · cited by 1
- Unitization.nnreal_cfcₙ_eq_cfc_inrproof · cited by 1
- CStarAlgebra.inr_map_Ici_zeroproof · cited by 1
- Unitization.LE.le.of_inrproof · cited by 1
- CStarAlgebra.inr_mem_Icc_iff_norm_leproof · cited by 1
- Unitization.sqrt_inrproof · cited by 0
- CStarAlgebra.norm_sub_mul_self_le_of_inrproof · cited by 0