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Theorems · Theorem · functional analysis

Prod.fst_exp

∀ {𝔸 : Type u_1} {𝔹 : Type u_2} [inst : NormedRing 𝔸] [NormedAlgebra ℚ 𝔸] [CompleteSpace 𝔸] [inst_3 : NormedRing 𝔹]
  [NormedAlgebra ℚ 𝔹] [CompleteSpace 𝔹] (x : 𝔸 × 𝔹), (NormedSpace.exp x).1 = NormedSpace.exp x.1
Defined in
Mathlib.Analysis.Normed.Algebra.Exponential
Cited by
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Foundations
Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedRingNormedAlgebraCompleteSpaceNormedRingNormedAlgebraCompleteSpace
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CompleteSpace · cited by 2532CompleteSpaceNormedAlgebra · cited by 1165NormedAlgebraNormedRing · cited by 924NormedRingNormedSpace.exp · cited by 157NormedSpace.expcontinuous_fst · cited by 103continuous_fstRingHom.fst · cited by 36RingHom.fstNormedSpace.map_exp · cited by 7NormedSpace.map_expProd.fst_expCITED BYCITES

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