Nuprl Lemma : es-interface-predecessors-cases
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
(≤(X)(e) ~ if e ∈b X then if first(e) then [e] else ≤(X)(pred(e)) @ [e] fi
if first(e) then []
else ≤(X)(pred(e))
fi )
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(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,
append: as @ bs,
cons: [a / b],
nil: [],
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Lemmas :
es-E_wf,
event-ordering+_subtype,
eclass_wf,
top_wf,
event-ordering+_wf,
es-first_wf2,
bool_wf,
list_ind_nil_lemma,
filter_cons_lemma,
filter_nil_lemma,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
in-eclass_wf,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
es-pred_wf,
append_back_nil,
append_wf,
filter_wf5,
es-before_wf,
l_member_wf,
cons_wf,
nil_wf,
filter_append_sq
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(\mleq{}(X)(e) \msim{} if e \mmember{}\msubb{} X then if first(e) then [e] else \mleq{}(X)(pred(e)) @ [e] fi
if first(e) then []
else \mleq{}(X)(pred(e))
fi )
Date html generated:
2015_07_20-PM-03_42_10
Last ObjectModification:
2015_01_27-PM-10_11_31
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