Nuprl Lemma : es-interface-sum-le-interface
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(ℤ)]. ∀[e:E]. (Σ≤e(X) = if e ∈b le(X) then Σ≤le(X)(e)(X) else 0 fi ∈ ℤ)
Proof
Definitions occuring in Statement :
es-interface-sum: Σ≤e(X),
es-le-interface: le(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],
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
top: Top,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s1;s2],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[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 ,
bfalse: ff,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
es-E-interface: E(X),
false: False,
not: ¬A,
or: P ∨ Q,
prop: ℙ
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(\mBbbZ{})]. \mforall{}[e:E].
(\mSigma{}\mleq{}e(X) = if e \mmember{}\msubb{} le(X) then \mSigma{}\mleq{}le(X)(e)(X) else 0 fi )
Date html generated:
2016_05_17-AM-08_10_39
Last ObjectModification:
2015_12_28-PM-11_14_01
Theory : event-ordering
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