Theorems · Theorem · functional analysis
RCLike.I_eq_zero_or_im_I_eq_one
∀ {K : Type u_1} [inst : RCLike K], RCLike.I = 0 ∨ RCLike.im RCLike.I = 1- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- map_negproof · cited by 378
- AddMonoid.toZerostatement · cited by 325
- RCLike.reproof · cited by 319
- RCLike.imstatement and proof · cited by 161
- RCLike.Istatement and proof · cited by 100
- RCLike.one_reproof · cited by 10
- RCLike.I_mul_reproof · cited by 3
- RCLike.I_mul_Iproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- RCLike.sqrt_neg_of_nonnegproof · cited by 1
- RCLike.sqrt_of_nonnegproof · cited by 1
- RCLike.norm_to_complexproof · cited by 1
- StrongDual.im_extendRCLike_applyproof · cited by 1
- RCLike.norm_le_im_iff_eq_I_mul_normproof · cited by 1
- RCLike.sqrt_eq_real_add_iteproof · cited by 0
- RCLike.sqrt_mapproof · cited by 0
- Module.Dual.im_extendRCLike_applyproof · cited by 0