Nuprl Lemma : es-interface-history-prior
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A List)]. ∀[e:E(X)].
(es-interface-history(es;X;e)
= if e ∈b prior(X) then es-interface-history(es;X;prior(X)(e)) @ X(e) else X(e) fi
∈ (A List))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-interface-history: es-interface-history(es;X;e),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
append: as @ bs,
list: T List,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top,
es-E-interface: E(X),
es-interface-history: es-interface-history(es;X;e),
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
es-locl: (e <loc e'),
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
prop: ℙ,
true: True,
rev_uimplies: rev_uimplies(P;Q),
exists: ∃x:A. B[x],
cand: A c∧ B,
in-eclass: e ∈b X,
eq_int: (i =z j),
bag-size: #(bs),
length: ||as||,
list_ind: list_ind,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
assert: ↑b,
mapfilter: mapfilter(f;P;L),
es-le: e ≤loc e' ,
or: P ∨ Q,
not: ¬A,
false: False,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
bnot: ¬bb,
es-interface-sublist: es-interface-sublist(X;z),
es-le-before: ≤loc(e),
concat: concat(ll)
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A List)]. \mforall{}[e:E(X)].
(es-interface-history(es;X;e)
= if e \mmember{}\msubb{} prior(X) then es-interface-history(es;X;prior(X)(e)) @ X(e) else X(e) fi )
Date html generated:
2016_05_17-AM-06_51_59
Last ObjectModification:
2016_01_17-PM-06_42_06
Theory : event-ordering
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