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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P),
or: P ∨ Q,
exists: ∃x:A. B[x],
guard: {T},
not: ¬A,
false: False,
es-p-le-pred: es-p-le-pred(es;P),
and: P ∧ Q
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:
2016_05_16-PM-11_17_09
Last ObjectModification:
2015_12_29-AM-10_29_24
Theory : event-ordering
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