Theorems · Theorem · functional analysis
RCLike.norm_I_of_ne_zero
∀ {K : Type u_1} [inst : RCLike K], RCLike.I ≠ 0 → ‖RCLike.I‖ = 1- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 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.
- Realstatement and proof · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- norm_nonnegproof · cited by 725
- zero_le_oneproof · cited by 316
- norm_negproof · cited by 190
- norm_mulproof · cited by 171
- NormOneClass.norm_oneproof · cited by 148
- RCLike.Istatement and proof · cited by 100
- mul_self_inj_of_nonnegproof · cited by 9
- RCLike.I_mul_I_of_nonzeroproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- InnerProductSpaceable.inner_.conj_symmproof · cited by 1
- RCLike.norm_le_im_iff_eq_I_mul_normproof · cited by 1