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
Lemmas :
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
es-le-interface-val-cases,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
in-eclass_wf,
bool_wf,
es-interface-sum_wf,
es-interface-sum-cases,
iff_weakening_equal,
eclass-val_wf2,
es-prior-interface_wf,
es-E-interface_wf,
es-is-le-interface-iff,
es-prior-interface_wf1
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:
2015_07_21-PM-04_21_22
Last ObjectModification:
2015_02_04-PM-06_04_42
Home
Index