Nuprl Lemma : iabgrp_op_inv_assoc_fps
∀[X:Type]. ∀[r:CRng]. ∀[a,b:PowerSeries(X;r)].
(((a+(-(a)+b)) = b ∈ PowerSeries(X;r)) ∧ ((-(a)+(a+b)) = b ∈ PowerSeries(X;r)))
Proof
Definitions occuring in Statement :
fps-neg: -(f),
fps-add: (f+g),
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
Lemmas referenced :
neg_assoc_fps,
power-series_wf,
crng_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
hypothesis,
independent_pairFormation,
because_Cache,
sqequalRule,
independent_pairEquality,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[r:CRng]. \mforall{}[a,b:PowerSeries(X;r)]. (((a+(-(a)+b)) = b) \mwedge{} ((-(a)+(a+b)) = b))
Date html generated:
2016_05_15-PM-09_50_01
Last ObjectModification:
2015_12_27-PM-04_39_36
Theory : power!series
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