Nuprl Lemma : only_value_of_sv_class_in_classrel
∀[Info,T:Type].
∀eo:EO+(Info). ∀[e:E]. ∀[v:T]. ∀[X:EClass(T)]. ((v ∈ X(e) ∧ Singlevalued(X)) ⇒ (v = only(X eo e) ∈ T))
Proof
Definitions occuring in Statement :
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,
apply: f a,
universe: Type,
equal: s = t ∈ T,
bag-only: only(bs)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
top: Top,
in-eclass: e ∈b X,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
nat: ℕ,
uiff: uiff(P;Q),
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
prop: ℙ
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{} (v = only(X eo e)))
Date html generated:
2016_05_17-AM-09_27_00
Last ObjectModification:
2016_01_17-PM-11_09_47
Theory : classrel!lemmas
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