Nuprl Lemma : member-class-at
∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[locs:bag(Id)]. uiff(↑e ∈b X@locs;(↑e ∈b X) ∧ loc(e) ↓∈ locs)
Proof
Definitions occuring in Statement :
class-at: X@locs,
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),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
bag-member: x ↓∈ bs,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
bag-size: #(bs),
rev_implies: P ⇐ Q,
eclass: EClass(A[eo; e]),
nat: ℕ,
class-at: X@locs,
cand: A c∧ B,
less_than: a < b,
less_than': less_than'(a;b),
length: ||as||,
list_ind: list_ind,
empty-bag: {},
nil: [],
it: ⋅,
false: False,
all: ∀x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
ifthenelse: if b then t else f fi ,
btrue: tt,
not: ¬A,
bfalse: ff,
bool: 𝔹,
unit: Unit
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[locs:bag(Id)].
uiff(\muparrow{}e \mmember{}\msubb{} X@locs;(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} loc(e) \mdownarrow{}\mmember{} locs)
Date html generated:
2016_05_17-AM-11_13_58
Last ObjectModification:
2016_01_18-AM-00_09_27
Theory : process-model
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