Nuprl Lemma : l-exists-decider_wf
∀[A:Type]. ∀[F:A ⟶ ℙ]. ∀L:A List. ∀dcd:∀k:A. Dec(F[k]). (l-exists-decider() L dcd ∈ Dec((∃k∈L. F[k])))
Proof
Definitions occuring in Statement :
l-exists-decider: l-exists-decider(),
l_exists: (∃x∈L. P[x]),
list: T List,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
decidable__l_exists,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x]
Lemmas referenced :
decidable__l_exists,
isect_wf,
list_wf,
decidable_wf,
l_exists_wf,
l_member_wf,
equal_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
instantiate,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
sqequalRule,
applyEquality,
lambdaEquality,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
setElimination,
rename,
setEquality,
dependent_functionElimination,
independent_functionElimination,
isectEquality,
because_Cache,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[A:Type]. \mforall{}[F:A {}\mrightarrow{} \mBbbP{}].
\mforall{}L:A List. \mforall{}dcd:\mforall{}k:A. Dec(F[k]). (l-exists-decider() L dcd \mmember{} Dec((\mexists{}k\mmember{}L. F[k])))
Date html generated:
2018_05_21-PM-00_36_07
Last ObjectModification:
2018_05_19-AM-06_43_16
Theory : list_1
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