Nuprl Lemma : sq_stable__l_member
∀[A:Type]. ∀x:A. ((∀x,y:A.  Dec(x = y ∈ A)) 
⇒ (∀L:A List. SqStable((x ∈ L))))
Proof
Definitions occuring in Statement : 
l_member: (x ∈ l)
, 
list: T List
, 
sq_stable: SqStable(P)
, 
decidable: Dec(P)
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
sq_stable_from_decidable, 
l_member_wf, 
decidable__l_member, 
list_wf, 
all_wf, 
decidable_wf, 
equal_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
lambdaFormation, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
independent_functionElimination, 
dependent_functionElimination, 
because_Cache, 
sqequalRule, 
lambdaEquality, 
universeEquality
Latex:
\mforall{}[A:Type].  \mforall{}x:A.  ((\mforall{}x,y:A.    Dec(x  =  y))  {}\mRightarrow{}  (\mforall{}L:A  List.  SqStable((x  \mmember{}  L))))
Date html generated:
2016_05_14-AM-06_43_17
Last ObjectModification:
2015_12_26-PM-00_28_32
Theory : list_0
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