Nuprl Lemma : es-interface-history-pred
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A:Type]. ∀[X:EClass(A List)]. ∀[e:E].
es-interface-history(es;X;e)
= if e ∈b X then es-interface-history(es;X;pred(e)) @ X(e) else es-interface-history(es;X;pred(e)) fi
∈ (A List)
supposing ¬↑first(e)
Proof
Definitions occuring in Statement :
es-interface-history: es-interface-history(es;X;e),
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,
append: as @ bs,
list: T List,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type,
equal: s = t ∈ T
Lemmas :
es-first_wf2,
event-ordering+_subtype,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
filter_cons_lemma,
filter_nil_lemma,
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_wf,
top_wf,
subtype_top,
list_wf,
map_cons_lemma,
map_nil_lemma,
reduce_nil_lemma,
append_wf,
squash_wf,
true_wf,
concat_wf,
mapfilter_wf,
es-before_wf,
eclass-val_wf,
es-E-interface-property,
concat-single,
subtype_rel_list,
append_nil_sq
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A:Type]. \mforall{}[X:EClass(A List)]. \mforall{}[e:E].
es-interface-history(es;X;e)
= if e \mmember{}\msubb{} X
then es-interface-history(es;X;pred(e)) @ X(e)
else es-interface-history(es;X;pred(e))
fi
supposing \mneg{}\muparrow{}first(e)
Date html generated:
2015_07_20-PM-03_39_28
Last ObjectModification:
2015_01_27-PM-10_14_14
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