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Theorems · Theorem · functional analysis

RCLike.norm_re_le_norm

∀ {K : Type u_1} [inst : RCLike K] (z : K), ‖RCLike.re z‖ ≤ ‖z‖
Defined in
Mathlib.Analysis.RCLike.Basic
Cited by
2 results in Mathlib
Foundations
Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLike
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.MemLp.re · cited by 2MemLp.reRCLike.lipschitzWith_re · cited by 1RCLike.lipschitzWith_reDFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealNorm.norm · cited by 5413Norm.normAddMonoidHom · cited by 3230AddMonoidHomRCLike · cited by 2829RCLikeAddMonoid.toZero · cited by 325AddMonoid.toZeroRCLike.re · cited by 319RCLike.reRCLike.abs_re_le_norm · cited by 6RCLike.abs_re_le_normRCLike.norm_re_le_normCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.