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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
Defined in
Mathlib.Analysis.Calculus.FormalMultilinearSeries
Cited by
39 results in Mathlib
Foundations
Depth 9 from the axioms · uses Quot.sound
Assumes
SemiringAddCommMonoidModuleTopologicalSpaceContinuousAddContinuousConstSMulAddCommMonoidModuleTopologicalSpaceContinuousAddContinuousConstSMul

Around this declaration

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

AnalyticAt.hasFPowerSeriesAt · cited by 7AnalyticAt.hasFPowerSerie…contDiffWithinAt_succ_iff_hasFDerivWithinAt · cited by 5contDiffWithinAt_succ_iff…FormalMultilinearSeries.ofScalars_comp_neg_id · cited by 3FormalMultilinearSeries.o…Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zero · cited by 3Complex.one_div_sub_pow_h…HasFPowerSeriesAt.eq_zero · cited by 2HasFPowerSeriesAt.eq_zerocompContinuousLinearMap_zero · cited by 2compContinuousLinearMap_z…Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zero · cited by 2Complex.one_div_one_sub_c…Real.one_div_sub_pow_hasFPowerSeriesOnBall_zero · cited by 2Real.one_div_sub_pow_hasF…hasFPowerSeriesAt_clog_one · cited by 2hasFPowerSeriesAt_clog_oneFormalMultilinearSeries.leftInv_comp · cited by 2FormalMultilinearSeries.l…PeriodPair.hasFPowerSeriesOnBall_derivWeierstrassPExcept · cited by 1PeriodPair.hasFPowerSerie…Real.hasFPowerSeriesOnBall_ofScalars_mul_add_zero · cited by 1Real.hasFPowerSeriesOnBal…FormalMultilinearSeries.ofScalars_sub · cited by 1FormalMultilinearSeries.o…constFormalMultilinearSeries_zero · cited by 1constFormalMultilinearSer…Complex.regularizedHGFunSeries_zero_zero · cited by 1Complex.regularizedHGFunS…TopologicalSpace · cited by 24529TopologicalSpaceModule · cited by 20661ModuleSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidContinuousMultilinearMap · cited by 1016ContinuousMultilinearMapContinuousConstSMul · cited by 832ContinuousConstSMulContinuousAdd · cited by 777ContinuousAddFormalMultilinearSeries · cited by 615FormalMultilinearSeriesFormalMultilinearSeries.extCITED BYCITES

Cites8

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Cited by39

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