Nuprl Lemma : prior-val-pred
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
(X)' es e ~ if pred(e) ∈b X then {X(pred(e))} else (X)' es pred(e) fi supposing ¬↑first(e)
Proof
Definitions occuring in Statement :
es-prior-val: (X)',
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-first: first(e),
es-pred: pred(e),
es-E: E,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
apply: f a,
universe: Type,
sqequal: s ~ t,
single-bag: {x}
Lemmas :
prior-val-cases,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
eqff_to_assert,
assert_of_bnot,
not_wf,
assert_wf,
es-first_wf2,
event-ordering+_subtype,
es-E_wf,
eclass_wf,
top_wf,
event-ordering+_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(X)' es e \msim{} if pred(e) \mmember{}\msubb{} X then \{X(pred(e))\} else (X)' es pred(e) fi supposing \mneg{}\muparrow{}first(e)
Date html generated:
2015_07_21-PM-03_20_23
Last ObjectModification:
2015_01_27-PM-06_45_37
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