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Theorems · Theorem · functional analysis

RCLike.im_ofReal_pow

∀ {K : Type u_1} [inst : RCLike K] (a : ℝ) (n : ℕ), RCLike.im (↑a ^ n) = 0
Defined in
Mathlib.Analysis.RCLike.Basic
Cited by
3 results in Mathlib
Foundations
Depth 160 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.

Matrix.posSemidef_gram · cited by 4Matrix.posSemidef_gramTensorProduct.norm_tmul · cited by 2TensorProduct.norm_tmulreal_inner_I_smul_self · cited by 0real_inner_I_smul_selfDFunLike.coe · cited by 62936DFunLike.coeReal · cited by 25697RealAddMonoidHom · cited by 3230AddMonoidHomRCLike · cited by 2829RCLikeRCLike.ofReal · cited by 350RCLike.ofRealAddMonoid.toZero · cited by 325AddMonoid.toZeroRCLike.im · cited by 161RCLike.imRCLike.ofReal_pow · cited by 9RCLike.ofReal_powRCLike.ofReal_im_ax · cited by 2RCLike.ofReal_im_axRCLike.im_ofReal_powCITED BYCITES

Cites9

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

Cited by3

Results whose statement or proof uses this declaration.