Nuprl Lemma : es-cut-locl-closed
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(Top)]. ∀[f:sys-antecedent(es;X)]. ∀[c:Cut(X;f)]. ∀[a,e:E(X)].
(e ∈ c) supposing ((e <loc a) and a ∈ c)
Proof
Definitions occuring in Statement :
es-cut: Cut(X;f),
sys-antecedent: sys-antecedent(es;Sys),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-locl: (e <loc e'),
es-eq: es-eq(es),
fset-member: a ∈ s,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type
Lemmas :
es-causl-swellfnd,
event-ordering+_subtype,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
fset-member_witness,
es-eq_wf-interface,
es-locl_wf,
fset-member_wf-cut,
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-E-interface_wf,
es-cut_wf,
sys-antecedent_wf,
eclass_wf,
top_wf,
es-E_wf,
event-ordering+_wf,
es-is-prior-interface,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert_wf,
eclass-val_wf2,
es-prior-interface_wf,
es-prior-interface-causl,
decidable__es-locl,
es-cut-closed-prior,
es-prior-interface-val,
es-locl-total2,
assert_functionality_wrt_uiff,
squash_wf,
true_wf,
not_assert_elim,
btrue_neq_bfalse
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(Top)]. \mforall{}[f:sys-antecedent(es;X)]. \mforall{}[c:Cut(X;f)].
\mforall{}[a,e:E(X)].
(e \mmember{} c) supposing ((e <loc a) and a \mmember{} c)
Date html generated:
2015_07_21-PM-03_55_41
Last ObjectModification:
2015_01_27-PM-05_57_57
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