Nuprl Lemma : es-interface-history-pred
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A List)]. ∀[e:E].
es-interface-history(es;X;e)
= if e ∈b X then es-interface-history(es;X;pred(e)) @ X(e) else es-interface-history(es;X;pred(e)) fi
∈ (A List)
supposing ¬↑first(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-first: first(e),
es-pred: pred(e),
es-E: E,
append: as @ bs,
list: T List,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
es-interface-history: es-interface-history(es;X;e),
es-le-before: ≤loc(e),
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-before: before(e),
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
mapfilter: mapfilter(f;P;L),
concat: concat(ll),
squash: ↓T,
in-eclass: e ∈b X,
eq_int: (i =z j),
bag-size: #(bs),
length: ||as||,
list_ind: list_ind,
es-E-interface: E(X),
true: True
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A List)]. \mforall{}[e:E].
es-interface-history(es;X;e)
= if e \mmember{}\msubb{} X
then es-interface-history(es;X;pred(e)) @ X(e)
else es-interface-history(es;X;pred(e))
fi
supposing \mneg{}\muparrow{}first(e)
Date html generated:
2016_05_16-PM-10_59_59
Last ObjectModification:
2016_01_17-PM-07_17_44
Theory : event-ordering
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