Nuprl Lemma : decidable__l_exists
∀[A:Type]. ∀[F:A ⟶ ℙ]. ∀L:A List. ((∀k:A. Dec(F[k])) ⇒ Dec((∃k∈L. F[k])))
Proof
Definitions occuring in Statement :
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],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
int_seg_decide: int_seg_decide(d;i;j),
it: ⋅,
genrec-ap: genrec-ap,
l-exists-decider: l-exists-decider(),
decidable__l_exists-proof,
decidable__exists_int_seg
Lemmas referenced :
decidable__l_exists-proof,
decidable__exists_int_seg
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[A:Type]. \mforall{}[F:A {}\mrightarrow{} \mBbbP{}]. \mforall{}L:A List. ((\mforall{}k:A. Dec(F[k])) {}\mRightarrow{} Dec((\mexists{}k\mmember{}L. F[k])))
Date html generated:
2018_05_21-PM-00_35_50
Last ObjectModification:
2018_05_19-AM-06_43_13
Theory : list_1
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