Nuprl Lemma : member-es-interface-history
∀[Info:Type]
∀es:EO+(Info)
∀[A:Type]
∀X:EClass(A List). ∀e:E. ∀a:A.
((a ∈ es-interface-history(es;X;e)) ⇐⇒ ∃e':E. (((↑e' ∈b X) ∧ e' ≤loc e ) ∧ (a ∈ X(e'))))
Proof
Definitions occuring in Statement :
es-interface-history: es-interface-history(es;X;e),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
l_member: (x ∈ l),
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
es-interface-history: es-interface-history(es;X;e),
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
cand: A c∧ B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
top: Top,
so_apply: x[s],
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
in-eclass: e ∈b X,
eq_int: (i =z j),
bag-size: #(bs),
length: ||as||,
list_ind: list_ind,
es-E-interface: E(X),
squash: ↓T
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A:Type]
\mforall{}X:EClass(A List). \mforall{}e:E. \mforall{}a:A.
((a \mmember{} es-interface-history(es;X;e)) \mLeftarrow{}{}\mRightarrow{} \mexists{}e':E. (((\muparrow{}e' \mmember{}\msubb{} X) \mwedge{} e' \mleq{}loc e ) \mwedge{} (a \mmember{} X(e'))))
Date html generated:
2016_05_16-PM-11_00_29
Last ObjectModification:
2016_01_17-PM-07_33_57
Theory : event-ordering
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