Nuprl Lemma : es-interface-set-subtype
∀[Info,A:Type]. ∀[P:A ─→ ℙ]. ∀[X:EClass(A)].
(X ∈ EClass({a:A| P[a]} )) supposing ((∀es:EO+(Info). ∀e:E(X). P[X(e)]) and Singlevalued(X))
Proof
Definitions occuring in Statement :
es-E-interface: E(X),
sv-class: Singlevalued(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
universe: Type
Lemmas :
all_wf,
event-ordering+_wf,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
sv-class_wf,
eclass_wf,
decidable__assert,
assert_wf,
bag_wf,
bag-only_wf2,
eq_int_wf,
bag-size_wf,
nat_wf,
le_wf,
not_wf,
assert_of_eq_int,
subtype-bag-only,
subtype_rel_bag,
decidable__lt,
false_wf,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
subtype_rel_sets,
equal_wf,
iff_weakening_equal,
single-valued-bag-if-le1,
neg_assert_of_eq_int,
subtype-bag-empty
\mforall{}[Info,A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbP{}]. \mforall{}[X:EClass(A)].
(X \mmember{} EClass(\{a:A| P[a]\} )) supposing ((\mforall{}es:EO+(Info). \mforall{}e:E(X). P[X(e)]) and Singlevalued(X))
Date html generated:
2015_07_17-PM-01_03_49
Last ObjectModification:
2015_02_04-PM-05_30_30
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