Nuprl Lemma : es-interface-predecessors-sqequal
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[X,Y:EClass(Top)]. ∀[e:E]. (≤(X)(e) ~ ≤(Y)(e)) supposing ∀e:E. (↑e ∈b X ⇐⇒ ↑e ∈b Y)
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-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
sqequal: s ~ t
Lemmas :
es-E_wf,
event-ordering+_subtype,
all_wf,
iff_wf,
assert_wf,
in-eclass_wf,
eclass_wf,
top_wf,
event-ordering+_wf,
append_wf,
es-before_wf,
cons_wf,
nil_wf,
list_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
equal-wf-T-base,
colength_wf_list,
list-cases,
filter_nil_lemma,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
nat_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
filter_cons_lemma,
bool_wf,
bool_subtype_base,
iff_imp_equal_bool,
es-E-interface-property
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X,Y:EClass(Top)].
\mforall{}[e:E]. (\mleq{}(X)(e) \msim{} \mleq{}(Y)(e)) supposing \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} X \mLeftarrow{}{}\mRightarrow{} \muparrow{}e \mmember{}\msubb{} Y)
Date html generated:
2015_07_21-PM-03_33_12
Last ObjectModification:
2015_01_27-PM-06_33_37
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