Theorems · Theorem · real analysis
contDiff_fst
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {n : WithTop ℕ∞},
ContDiff 𝕜 n Prod.fstThe first projection in a product is C^∞.
- Defined in
- Mathlib.Analysis.Calculus.ContDiff.Comp
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ENatstatement and proof · cited by 4,985
- WithTopstatement and proof · cited by 3,754
- ContDiffstatement · cited by 352
- IsBoundedLinearMap.contDiffproof · cited by 6
- IsBoundedLinearMap.fstproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- contDiffAt_fstproof · cited by 7
- ContMDiffWithinAt.clm_applyproof · cited by 5
- contDiffOn_fstproof · cited by 3
- contDiffWithinAt_fstproof · cited by 3
- ContMDiffWithinAt.clm_compproof · cited by 3
- ContDiff.fstproof · cited by 3
- ContDiffOn.fstproof · cited by 2
- ContDiffWithinAt.fderivWithin_applyproof · cited by 1
- ContDiff.fst'proof · cited by 0