Theorems · Theorem · complex analysis
FormalMultilinearSeries.ofScalars.congr_simp
∀ {𝕜 : Type u_1} (E : Type u_2) [inst : Field 𝕜] [inst_1 : Ring E] [inst_2 : Algebra 𝕜 E] [inst_3 : TopologicalSpace E]
[inst_4 : IsTopologicalRing E] (c c_1 : ℕ → 𝕜),
c = c_1 → ∀ (n : ℕ), FormalMultilinearSeries.ofScalars E c n = FormalMultilinearSeries.ofScalars E c_1 n- Defined in
- Mathlib.Analysis.Analytic.OfScalars
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- ContinuousMultilinearMapstatement · cited by 1,016
- IsTopologicalRingstatement and proof · cited by 402
- FormalMultilinearSeries.ofScalarsstatement and proof · cited by 68
Cited by6
Results whose statement or proof uses this declaration.
- Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zeroproof · cited by 3
- PeriodPair.summable_weierstrassPExceptSummandproof · cited by 3
- Real.one_div_sub_pow_hasFPowerSeriesOnBall_zeroproof · cited by 2
- Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 2
- Complex.one_div_sub_sq_sub_one_div_sq_hasFPowerSeriesOnBall_zeroproof · cited by 1
- PeriodPair.weierstrassPExcept_eq_tsumproof · cited by 1