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Theorems · Theorem · real analysis

differentiable_fst

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type u_3} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F],
  Differentiable 𝕜 Prod.fst
Defined in
Mathlib.Analysis.Calculus.FDeriv.Prod
Cited by
6 results in Mathlib
Foundations
Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace
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Around this declaration

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

MDifferentiableWithinAt.clm_apply · cited by 3MDifferentiableWithinAt.c…MDifferentiableWithinAt.clm_comp · cited by 3MDifferentiableWithinAt.c…MDifferentiableAt.clm_apply · cited by 1MDifferentiableAt.clm_app…differentiableOn_fst · cited by 0differentiableOn_fstDifferentiable.fst · cited by 0Differentiable.fstDifferentiableOn.fst · cited by 0DifferentiableOn.fstNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceNontriviallyNormedField · cited by 8742NontriviallyNormedFieldDifferentiable · cited by 298DifferentiabledifferentiableAt_fst · cited by 5differentiableAt_fstdifferentiable_fstCITED BYCITES

Cites5

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Cited by6

Results whose statement or proof uses this declaration.