### 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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