Nuprl Lemma : decidable__exists-es-p-le-pred
∀es:EO. ∀[P:E ⟶ ℙ]. ∀e:E. ((∀e:E. Dec(P e)) ⇒ Dec(∃a:E. (es-p-le-pred(es;P) e a)))
Proof
Definitions occuring in Statement :
es-p-le-pred: es-p-le-pred(es;P),
es-E: E,
event_ordering: EO,
decidable: Dec(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
es-p-le-pred: es-p-le-pred(es;P),
and: P ∧ Q,
cand: A c∧ B,
existse-le: ∃e≤e'.P[e],
alle-le: ∀e≤e'.P[e],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
alle-at: ∀e@i.P[e]
Latex:
\mforall{}es:EO. \mforall{}[P:E {}\mrightarrow{} \mBbbP{}]. \mforall{}e:E. ((\mforall{}e:E. Dec(P e)) {}\mRightarrow{} Dec(\mexists{}a:E. (es-p-le-pred(es;P) e a)))
Date html generated:
2016_05_16-AM-10_08_51
Last ObjectModification:
2015_12_28-PM-09_26_50
Theory : new!event-ordering
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