Nuprl Lemma : decidable__l_exists_better-extract
∀[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
Lemmas referenced :
decidable__l_exists
Rules used in proof :
cut,
lemma_by_obid,
hypothesis
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:
2016_05_15-PM-04_20_06
Last ObjectModification:
2015_12_27-PM-02_55_22
Theory : general
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