Theorems · Theorem · functional analysis
FormalMultilinearSeries.ext
∀ {𝕜 : Type u} {E : Type v} {F : Type w} [inst : Semiring 𝕜] [inst_1 : AddCommMonoid E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [inst_4 : ContinuousAdd E] [inst_5 : ContinuousConstSMul 𝕜 E] [inst_6 : AddCommMonoid F]
[inst_7 : Module 𝕜 F] [inst_8 : TopologicalSpace F] [inst_9 : ContinuousAdd F] [inst_10 : ContinuousConstSMul 𝕜 F]
{p q : FormalMultilinearSeries 𝕜 E F}, (∀ (n : ℕ), p n = q n) → p = q- Cited by
- 39 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses 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.
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- ContinuousMultilinearMapstatement · cited by 1,016
- ContinuousConstSMulstatement and proof · cited by 832
- ContinuousAddstatement and proof · cited by 777
- FormalMultilinearSeriesstatement and proof · cited by 615
Cited by39
Results whose statement or proof uses this declaration.
- AnalyticAt.hasFPowerSeriesAtproof · cited by 7
- contDiffWithinAt_succ_iff_hasFDerivWithinAtproof · cited by 5
- FormalMultilinearSeries.ofScalars_comp_neg_idproof · cited by 3
- Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zeroproof · cited by 3
- HasFPowerSeriesAt.eq_zeroproof · cited by 2
- compContinuousLinearMap_zeroproof · cited by 2
- Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 2
- Real.one_div_sub_pow_hasFPowerSeriesOnBall_zeroproof · cited by 2
- hasFPowerSeriesAt_clog_oneproof · cited by 2
- FormalMultilinearSeries.leftInv_compproof · cited by 2
- PeriodPair.hasFPowerSeriesOnBall_derivWeierstrassPExceptproof · cited by 1
- Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zeroproof · cited by 1