Nuprl Lemma : eclass-ext
∀[T:Type]. ∀[A:es:EO+(T) ⟶ E ⟶ Type]. ∀[X,Y:EClass(A[es;e])].
X = Y ∈ EClass(A[es;e]) supposing ∀es:EO+(T). ∀e:E. ((X es e) = (Y es e) ∈ bag(A[es;e]))
Proof
Definitions occuring in Statement :
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
bag: bag(T)
Definitions unfolded in proof :
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Latex:
\mforall{}[T:Type]. \mforall{}[A:es:EO+(T) {}\mrightarrow{} E {}\mrightarrow{} Type]. \mforall{}[X,Y:EClass(A[es;e])].
X = Y supposing \mforall{}es:EO+(T). \mforall{}e:E. ((X es e) = (Y es e))
Date html generated:
2016_05_16-PM-01_26_27
Last ObjectModification:
2015_12_29-PM-02_02_50
Theory : event-ordering
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