### Nuprl Lemma : decidable__l_member

`∀[A:Type]. ∀x:A. ((∀x,y:A.  Dec(x = y ∈ A)) `` (∀L:A List. Dec((x ∈ L))))`

Proof

Definitions occuring in Statement :  l_member: `(x ∈ l)` list: `T List` 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` so_lambda: `λ2x.t[x]` so_apply: `x[s]` iff: `P `⇐⇒` Q` and: `P ∧ Q` rev_implies: `P `` Q` prop: `ℙ`
Lemmas referenced :  list_induction decidable_wf l_member_wf list_wf decidable_functionality nil_wf false_wf nil_member decidable__false cons_wf or_wf equal_wf cons_member decidable__or all_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation lambdaFormation cut thin lemma_by_obid sqequalHypSubstitution isectElimination because_Cache sqequalRule lambdaEquality hypothesisEquality hypothesis independent_functionElimination dependent_functionElimination productElimination rename universeEquality

Latex:
\mforall{}[A:Type].  \mforall{}x:A.  ((\mforall{}x,y:A.    Dec(x  =  y))  {}\mRightarrow{}  (\mforall{}L:A  List.  Dec((x  \mmember{}  L))))

Date html generated: 2016_05_14-AM-06_43_14
Last ObjectModification: 2015_12_26-PM-00_28_44

Theory : list_0

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