Nuprl Lemma : member-eclass-simple-loc-comb-1
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[F:Id ⟶ bag(A) ⟶ bag(B)]. ∀[X:EClass(A)].
(↑e ∈b F(Loc, X)) supposing ((∀loc:Id. ∀as:bag(A). ((¬↑bag-null(as)) ⇒ (¬↑bag-null(F loc as)))) and (↑e ∈b X))
Proof
Definitions occuring in Statement :
simple-loc-comb-1: F(Loc, X),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
bag-null: bag-null(bs),
bag: bag(T)
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2],
uimplies: b supposing a,
eclass: EClass(A[eo; e]),
not: ¬A,
top: Top,
iff: P ⇐⇒ Q,
and: P ∧ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
false: False,
member-eclass: e ∈b X,
simple-loc-comb-1: F(Loc, X),
simple-loc-comb: F|Loc; Xs|,
select: L[n],
cons: [a / b],
uiff: uiff(P;Q),
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[F:Id {}\mrightarrow{} bag(A) {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)].
(\muparrow{}e \mmember{}\msubb{} F(Loc, X)) supposing
((\mforall{}loc:Id. \mforall{}as:bag(A). ((\mneg{}\muparrow{}bag-null(as)) {}\mRightarrow{} (\mneg{}\muparrow{}bag-null(F loc as)))) and
(\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2016_05_17-AM-11_14_05
Last ObjectModification:
2015_12_29-PM-05_12_40
Theory : process-model
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