Nuprl Lemma : es-interface-restrict-conditional
∀[Info,A:Type]. ∀[I:EClass(A)]. ∀[P:es:EO+(Info) ⟶ E ⟶ ℙ]. ∀[p:∀es:EO+(Info). ∀e:E. Dec(P[es;e])].
[(I|p)?(I|¬p)] = I ∈ EClass(A) supposing Singlevalued(I)
Proof
Definitions occuring in Statement :
es-interface-co-restrict: (I|¬p),
es-interface-restrict: (I|p),
cond-class: [X?Y],
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
decidable: Dec(P),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
eclass: EClass(A[eo; e]),
es-interface-co-restrict: (I|¬p),
es-interface-restrict: (I|p),
cond-class: [X?Y],
eclass-compose2: eclass-compose2(f;X;Y),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
bfalse: ff,
so_lambda: λ2x y.t[x; y],
iff: P ⇐⇒ Q,
and: P ∧ Q
Latex:
\mforall{}[Info,A:Type]. \mforall{}[I:EClass(A)]. \mforall{}[P:es:EO+(Info) {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}].
\mforall{}[p:\mforall{}es:EO+(Info). \mforall{}e:E. Dec(P[es;e])].
[(I|p)?(I|\mneg{}p)] = I supposing Singlevalued(I)
Date html generated:
2016_05_16-PM-10_50_21
Last ObjectModification:
2015_12_29-AM-10_48_30
Theory : event-ordering
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