Nuprl Lemma : es-interface-accum-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[b,f:Top]. ∀[e:E].
es-interface-accum(f;b;X)(e) ~ accumulate (with value b and list item e):
f b X(e)
over list:
≤(X)(e)
with starting value:
b)
supposing ↑e ∈b es-interface-accum(f;b;X)
Proof
Definitions occuring in Statement :
es-interface-accum: es-interface-accum(f;x;X),
es-interface-predecessors: ≤(X)(e),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
list_accum: list_accum,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
eclass-val: X(e),
es-interface-accum: es-interface-accum(f;x;X),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
nat: ℕ,
all: ∀x:A. B[x],
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 ,
top: Top,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
eq_int: (i =z j)
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[b,f:Top]. \mforall{}[e:E].
es-interface-accum(f;b;X)(e) \msim{} accumulate (with value b and list item e):
f b X(e)
over list:
\mleq{}(X)(e)
with starting value:
b)
supposing \muparrow{}e \mmember{}\msubb{} es-interface-accum(f;b;X)
Date html generated:
2016_05_16-PM-11_06_55
Last ObjectModification:
2015_12_29-AM-10_37_24
Theory : event-ordering
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