Nuprl Lemma : classrel-classfun
∀[Info,T:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(T)]. ∀[e:E]. ∀[v:T]. uiff(v ∈ X(e);v = X(e) ∈ T) supposing X is functional
Proof
Definitions occuring in Statement :
classfun: X(e),
es-functional-class: X is functional,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[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,
uiff: uiff(P;Q),
and: P ∧ Q,
es-functional-class: X is functional,
single-valued-classrel: single-valued-classrel(es;X;T),
all: ∀x:A. B[x],
es-total-class: es-total-class(es;X),
implies: P ⇒ Q,
classrel: v ∈ X(e),
prop: ℙ,
bag-member: x ↓∈ bs,
squash: ↓T,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,T:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T)].
\mforall{}[e:E]. \mforall{}[v:T]. uiff(v \mmember{} X(e);v = X(e)) supposing X is functional
Date html generated:
2016_05_16-PM-01_44_10
Last ObjectModification:
2016_01_17-PM-07_48_44
Theory : event-ordering
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