Nuprl Lemma : es-interface-predecessors-step-sq
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[e:E].
(≤(X)(e) ~ if e ∈b prior(X) then ≤(X)(prior(X)(e)) else [] fi @ if e ∈b X then [e] else [] fi )
Proof
Definitions occuring in Statement :
es-prior-interface: prior(X),
es-interface-predecessors: ≤(X)(e),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
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-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
nat_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul,
es-interface-predecessors-cases,
in-eclass_wf,
es-prior-interface_wf0,
es-interface-subtype_rel2,
subtype_top,
bool_wf,
eqtt_to_assert,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
list_ind_nil_lemma,
es-prior-interface-cases-sq,
es-first_wf2,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
append_back_nil,
es-E-interface_wf,
Id_wf,
es-loc_wf,
es-pred_wf,
es-interface-predecessors_wf,
es-pred-locl,
es-causl_weakening,
eclass-val_wf2,
es-prior-interface_wf,
es-interface-predecessors-nil
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[e:E].
(\mleq{}(X)(e) \msim{} if e \mmember{}\msubb{} prior(X) then \mleq{}(X)(prior(X)(e)) else [] fi @ if e \mmember{}\msubb{} X then [e] else [] fi )
Date html generated:
2015_07_21-PM-03_32_48
Last ObjectModification:
2015_01_27-PM-06_40_03
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