Nuprl Lemma : fps-neg-slice

[X:Type]. ∀[r:CRng]. ∀[n:ℤ]. ∀[g:PowerSeries(X;r)].  ([-(g)]_n -([g]_n) ∈ PowerSeries(X;r))


Proof




Definitions occuring in Statement :  fps-slice: [f]_n fps-neg: -(f) power-series: PowerSeries(X;r) uall: [x:A]. B[x] int: universe: Type equal: t ∈ T crng: CRng
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a all: x:A. B[x] fps-slice: [f]_n fps-neg: -(f) fps-coeff: f[b] subtype_rel: A ⊆B implies:  Q bool: 𝔹 unit: Unit it: btrue: tt nat: ifthenelse: if then else fi  crng: CRng rng: Rng power-series: PowerSeries(X;r) bfalse: ff exists: x:A. B[x] prop: or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b false: False squash: T true: True iff: ⇐⇒ Q rev_implies:  Q
Lemmas referenced :  fps-ext fps-slice_wf fps-neg_wf eq_int_wf bag-size_wf bool_wf eqtt_to_assert assert_of_eq_int nat_wf rng_minus_wf eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int squash_wf true_wf rng_car_wf rng_zero_wf rng_minus_zero iff_weakening_equal bag_wf power-series_wf crng_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality cumulativity hypothesis productElimination independent_isectElimination lambdaFormation sqequalRule applyEquality because_Cache unionElimination equalityElimination equalityTransitivity equalitySymmetry lambdaEquality setElimination rename dependent_pairFormation promote_hyp dependent_functionElimination instantiate independent_functionElimination voidElimination imageElimination natural_numberEquality imageMemberEquality baseClosed universeEquality isect_memberEquality axiomEquality intEquality

Latex:
\mforall{}[X:Type].  \mforall{}[r:CRng].  \mforall{}[n:\mBbbZ{}].  \mforall{}[g:PowerSeries(X;r)].    ([-(g)]\_n  =  -([g]\_n))



Date html generated: 2018_05_21-PM-09_56_08
Last ObjectModification: 2017_07_26-PM-06_32_54

Theory : power!series


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