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
Lemmas :
es-E_wf,
event-ordering+_subtype,
eclass_wf,
event-ordering+_wf,
in-eclass_wf,
es-interface-subtype_rel2,
top_wf,
subtype_top,
bool_wf,
eqtt_to_assert,
es-prior-interface_wf1,
es-E-interface_wf,
es-interface-local-state_wf,
eclass-val_wf2,
es-prior-interface_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
eclass-val_wf,
es-interface-local-state-cases,
iff_weakening_equal
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:
2015_07_21-PM-03_44_16
Last ObjectModification:
2015_02_04-PM-06_10_46
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