### Nuprl Lemma : negerse_fps

`∀[X:Type]. ∀[r:CRng]. ∀[a:PowerSeries(X;r)].  (((a+-(a)) = 0 ∈ PowerSeries(X;r)) ∧ ((-(a)+a) = 0 ∈ PowerSeries(X;r)))`

Proof

Definitions occuring in Statement :  fps-neg: `-(f)` fps-add: `(f+g)` fps-zero: `0` power-series: `PowerSeries(X;r)` uall: `∀[x:A]. B[x]` and: `P ∧ Q` universe: `Type` equal: `s = t ∈ T` crng: `CRng`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` and: `P ∧ Q` cand: `A c∧ B` squash: `↓T` prop: `ℙ` true: `True` subtype_rel: `A ⊆r B` uimplies: `b supposing a` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` implies: `P `` Q` fps-zero: `0` fps-neg: `-(f)` fps-add: `(f+g)` power-series: `PowerSeries(X;r)` fps-coeff: `f[b]` crng: `CRng` rng: `Rng` infix_ap: `x f y`
Lemmas referenced :  equal_wf squash_wf true_wf power-series_wf fps-add-comm fps-neg_wf iff_weakening_equal crng_wf bag_wf rng_car_wf rng_zero_wf rng_plus_inv
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut independent_pairFormation hypothesis applyEquality thin lambdaEquality sqequalHypSubstitution imageElimination extract_by_obid isectElimination hypothesisEquality equalityTransitivity equalitySymmetry universeEquality cumulativity natural_numberEquality sqequalRule imageMemberEquality baseClosed independent_isectElimination productElimination independent_functionElimination independent_pairEquality axiomEquality isect_memberEquality because_Cache functionExtensionality setElimination rename

Latex:
\mforall{}[X:Type].  \mforall{}[r:CRng].  \mforall{}[a:PowerSeries(X;r)].    (((a+-(a))  =  0)  \mwedge{}  ((-(a)+a)  =  0))

Date html generated: 2018_05_21-PM-09_56_35
Last ObjectModification: 2017_07_26-PM-06_32_59

Theory : power!series

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