Nuprl Lemma : member-eclass-eclass0
∀[Info,B,C:Type]. ∀[X:EClass(B)]. ∀[f:Id ⟶ B ⟶ bag(C)]. ∀[es:EO+(Info)]. ∀[e:E].
uiff(↑e ∈b (f o X);(↑e ∈b X) ∧ (¬↑bag-null(f loc(e) X@e))) supposing single-valued-classrel(es;X;B)
Proof
Definitions occuring in Statement :
eclass0: (f o X),
classfun-res: X@e,
single-valued-classrel: single-valued-classrel(es;X;T),
member-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
assert: ↑b,
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
bag-null: bag-null(bs),
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
exists: ∃x:A. B[x],
uiff: uiff(P;Q),
uimplies: b supposing a,
prop: ℙ,
not: ¬A,
false: False,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B)]. \mforall{}[f:Id {}\mrightarrow{} B {}\mrightarrow{} bag(C)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} (f o X);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\mneg{}\muparrow{}bag-null(f loc(e) X@e)))
supposing single-valued-classrel(es;X;B)
Date html generated:
2016_05_17-AM-11_14_49
Last ObjectModification:
2016_01_18-AM-00_09_44
Theory : process-model
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