Theorems · Theorem · functional analysis
RCLike.re_ofReal_pow
∀ {K : Type u_1} [inst : RCLike K] (a : ℝ) (n : ℕ), RCLike.re (↑a ^ n) = a ^ n- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 160 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.
Cites9
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 and proof · cited by 25,697
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- RCLike.ofRealstatement · cited by 350
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
- RCLike.ofReal_reproof · cited by 60
- RCLike.ofReal_powproof · cited by 9
Cited by7
Results whose statement or proof uses this declaration.
- Matrix.posSemidef_gramproof · cited by 4
- TensorProduct.norm_tmulproof · cited by 2
- re_inner_self_nonposproof · cited by 2
- re_inner_self_posproof · cited by 1
- eq_of_norm_le_re_inner_eq_norm_sqproof · cited by 1
- ContinuousLinearMap.tendsto_birkhoffAverage_orthogonalProjectionproof · cited by 0
- real_inner_I_smul_selfproof · cited by 0