Nuprl Lemma : es-interface-sum-cases
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(ℤ)]. ∀[e:E].
(Σ≤e(X)
= if e ∈b X then if e ∈b prior(X) then Σ≤prior(X)(e)(X) else 0 fi + X(e)
if e ∈b prior(X) then Σ≤prior(X)(e)(X)
else 0
fi
∈ ℤ)
Proof
Definitions occuring in Statement :
es-interface-sum: Σ≤e(X),
es-prior-interface: prior(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
es-interface-sum: Σ≤e(X),
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,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
es-E-interface: E(X),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(\mBbbZ{})]. \mforall{}[e:E].
(\mSigma{}\mleq{}e(X)
= if e \mmember{}\msubb{} X then if e \mmember{}\msubb{} prior(X) then \mSigma{}\mleq{}prior(X)(e)(X) else 0 fi + X(e)
if e \mmember{}\msubb{} prior(X) then \mSigma{}\mleq{}prior(X)(e)(X)
else 0
fi )
Date html generated:
2016_05_17-AM-07_12_11
Last ObjectModification:
2015_12_29-AM-00_06_15
Theory : event-ordering
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