Nuprl Lemma : decidable-exists-finite
∀[T:Type]. ∀[P:T ─→ ℙ]. ((∀x:T. Dec(P[x])) ⇒ finite-type(T) ⇒ Dec(∃x:T. P[x]))
Proof
Definitions occuring in Statement :
finite-type: finite-type(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
finite-type_wf,
all_wf,
decidable_wf,
exists_wf,
int_seg_wf,
iff_weakening_equal,
decidable_functionality,
decidable__exists_int_seg
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. ((\mforall{}x:T. Dec(P[x])) {}\mRightarrow{} finite-type(T) {}\mRightarrow{} Dec(\mexists{}x:T. P[x]))
Date html generated:
2015_07_17-AM-09_05_09
Last ObjectModification:
2015_02_04-PM-06_27_35
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