Theorems · Theorem · functional analysis
CFC.sqrt.congr_simp
∀ {A : Type u_1} [inst : PartialOrder A] [inst_1 : NonUnitalRing A] [inst_2 : TopologicalSpace A] [inst_3 : StarRing A]
[inst_4 : Module ℝ A] [inst_5 : SMulCommClass ℝ A A] [inst_6 : IsScalarTower ℝ A A] [inst_7 : StarOrderedRing A]
[inst_8 : NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_9 : NonnegSpectrumClass ℝ A] (a a_1 : A),
a = a_1 → CFC.sqrt a = CFC.sqrt a_1- Cited by
- 8 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- PartialOrderstatement and proof · cited by 6,410
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- NonUnitalRingstatement and proof · cited by 422
- NonnegSpectrumClassstatement and proof · cited by 292
- NonUnitalContinuousFunctionalCalculusstatement and proof · cited by 275
Cited by8
Results whose statement or proof uses this declaration.
- CFC.abs_negproof · cited by 2
- CFC.abs_smulproof · cited by 1
- CFC.abs_coe_unitaryproof · cited by 1
- CFC.abs_starproof · cited by 0
- CFC.abs_zeroproof · cited by 0
- CFC.sqrt_ringInverseproof · cited by 0
- CFC.sqrt_rpowproof · cited by 0
- CFC.sqrt_rpow_nnrealproof · cited by 0