Nuprl Lemma : member-eclass-simple-comb-1
∀[Info,A,B:Type]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[F:bag(A) ⟶ bag(B)]. ∀[X:EClass(A)].
(↑e ∈b F|X|) supposing ((∀as:bag(A). ((¬↑bag-null(as)) ⇒ (¬↑bag-null(F as)))) and (↑e ∈b X))
Proof
Definitions occuring in Statement :
simple-comb-1: F|X|,
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
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 :
all: ∀x:A. B[x],
member: t ∈ T,
eclass: EClass(A[eo; e]),
implies: P ⇒ Q,
not: ¬A,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
top: Top,
iff: P ⇐⇒ Q,
and: P ∧ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
false: False,
prop: ℙ,
member-eclass: e ∈b X,
simple-comb-1: F|X|,
simple-comb: simple-comb(F;Xs),
select: L[n],
cons: [a / b],
uiff: uiff(P;Q),
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[F:bag(A) {}\mrightarrow{} bag(B)]. \mforall{}[X:EClass(A)].
(\muparrow{}e \mmember{}\msubb{} F|X|) supposing ((\mforall{}as:bag(A). ((\mneg{}\muparrow{}bag-null(as)) {}\mRightarrow{} (\mneg{}\muparrow{}bag-null(F as)))) and (\muparrow{}e \mmember{}\msubb{} X))
Date html generated:
2016_05_17-AM-11_12_54
Last ObjectModification:
2015_12_29-PM-05_14_20
Theory : process-model
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