Nuprl Lemma : es-interface-predecessors-step
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E(X)].
(≤(X)(e) = if e ∈b prior(X) then ≤(X)(prior(X)(e)) @ [e] else [e] fi ∈ ({a:E(X)| loc(a) = loc(e) ∈ Id} List))
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
Id: Id,
append: as @ bs,
cons: [a / b],
nil: [],
list: T List,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Lemmas :
es-interface-predecessors-step-sq,
in-eclass_wf,
es-prior-interface_wf0,
bool_wf,
eqtt_to_assert,
append_wf,
Id_wf,
es-loc_wf,
event-ordering+_subtype,
es-interface-predecessors_wf,
eclass-val_wf2,
es-prior-interface_wf,
subtype_rel_list_set,
es-loc-prior-interface,
iff_weakening_equal,
equal_wf,
cons_wf,
nil_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
assert_elim,
not_assert_elim,
btrue_neq_bfalse,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_wf,
top_wf,
subtype_top,
list_ind_nil_lemma,
es-E-interface_wf,
eclass_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E(X)].
(\mleq{}(X)(e) = if e \mmember{}\msubb{} prior(X) then \mleq{}(X)(prior(X)(e)) @ [e] else [e] fi )
Date html generated:
2015_07_21-PM-03_33_00
Last ObjectModification:
2015_02_04-PM-06_13_45
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