Nuprl Lemma : event_in_sv_classrel_is_in_class
∀[Info,T:Type]. ∀eo:EO+(Info). ∀[e:E]. ∀[v:T]. ∀[X:EClass(T)]. ((v ∈ X(e) ∧ Singlevalued(X)) ⇒ (e ∈ E(X)))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
sv-class: Singlevalued(X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
and: P ∧ Q,
es-E-interface: E(X),
in-eclass: e ∈b X,
classrel: v ∈ X(e),
sv-class: Singlevalued(X),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
eclass: EClass(A[eo; e]),
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
guard: {T},
prop: ℙ,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
sq_type: SQType(T),
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
assert: ↑b,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
btrue: tt,
true: True,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,T:Type].
\mforall{}eo:EO+(Info). \mforall{}[e:E]. \mforall{}[v:T]. \mforall{}[X:EClass(T)]. ((v \mmember{} X(e) \mwedge{} Singlevalued(X)) {}\mRightarrow{} (e \mmember{} E(X)))
Date html generated:
2016_05_17-AM-09_26_56
Last ObjectModification:
2016_01_17-PM-11_09_51
Theory : classrel!lemmas
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