Nuprl Lemma : es-interface-le-pred
∀[Info:Type]. ∀[P:es:EO+(Info) ─→ E ─→ ℙ].
((∀es:EO+(Info). ∀e:E. Dec(P es e))
⇒ (∃X:EClass({e:E| P es e} )
∀es:EO+(Info). ∀e:E.
((↑e ∈b X ⇐⇒ ∃a:{e:E| P es e} . (es-p-le-pred(es;P es) e a))
∧ es-p-le-pred(es;P es) e X(e) supposing ↑e ∈b X)))
Proof
Definitions occuring in Statement :
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-p-le-pred: es-p-le-pred(es;P),
es-E: E,
assert: ↑b,
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
universe: Type
Lemmas :
es-interface-from-decidable,
es-E_wf,
event-ordering+_subtype,
es-p-le-pred_wf,
all_wf,
event-ordering+_wf,
decidable_wf,
decidable__exists-es-p-le-pred,
not_wf,
exists_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}].
((\mforall{}es:EO+(Info). \mforall{}e:E. Dec(P es e))
{}\mRightarrow{} (\mexists{}X:EClass(\{e:E| P es e\} )
\mforall{}es:EO+(Info). \mforall{}e:E.
((\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \mexists{}a:\{e:E| P es e\} . (es-p-le-pred(es;P es) e a))
\mwedge{} es-p-le-pred(es;P es) e X(e) supposing \muparrow{}e \mmember{}\msubb{} X)))
Date html generated:
2015_07_20-PM-03_56_04
Last ObjectModification:
2015_01_27-PM-09_59_31
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