Nuprl Lemma : es-interface-le-pred-bool
∀[Info:Type]
∀P:es:EO+(Info) ─→ E ─→ 𝔹
∃X:EClass({e:E| ↑(P es e)} )
∀es:EO+(Info). ∀e:E.
((↑e ∈b X ⇐⇒ ∃a:E. (es-p-le-pred(es;λe.(↑(P es e))) e a))
∧ es-p-le-pred(es;λe.(↑(P es e))) 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,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
es-interface-le-pred,
assert_wf,
es-E_wf,
event-ordering+_subtype,
decidable__assert,
event-ordering+_wf,
bool_wf,
es-le_wf,
all_wf,
es-locl_wf,
not_wf,
exists_wf,
in-eclass_wf,
es-interface-subtype_rel2,
top_wf,
subtype_top,
iff_wf,
eclass-val_wf
Latex:
\mforall{}[Info:Type]
\mforall{}P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbB{}
\mexists{}X:EClass(\{e:E| \muparrow{}(P es e)\} )
\mforall{}es:EO+(Info). \mforall{}e:E.
((\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \mexists{}a:E. (es-p-le-pred(es;\mlambda{}e.(\muparrow{}(P es e))) e a))
\mwedge{} es-p-le-pred(es;\mlambda{}e.(\muparrow{}(P es e))) e X(e) supposing \muparrow{}e \mmember{}\msubb{} X)
Date html generated:
2015_07_20-PM-03_56_22
Last ObjectModification:
2015_01_27-PM-09_59_55
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