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: List sq_stable: SqStable(P) decidable: Dec(P) uall: [x:A]. B[x] all: x:A. B[x] implies:  Q universe: Type equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] all: x:A. B[x] implies:  Q member: t ∈ T prop: 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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