Nuprl Lemma : is-tagged-true
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[T:Type]. ∀[X:EClass(T × 𝔹)]. ∀[e:E].
uiff(↑e ∈b Tagged_tt(X);(↑e ∈b X) ∧ (↑(snd(X(e)))))
Proof
Definitions occuring in Statement :
es-tagged-true-class: Tagged_tt(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
bool: 𝔹,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
pi2: snd(t),
and: P ∧ Q,
product: x:A × B[x],
universe: Type
Lemmas :
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
subtype_top,
bool_wf,
eclass-val_wf,
assert_wf,
es-tagged-true-class_wf,
subtype_rel_product,
subtype_rel_self,
eclass_wf,
eqtt_to_assert,
assert_witness,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
false_wf,
iff_weakening_uiff,
es-filter-image_wf,
single-bag_wf,
empty-bag_wf,
equal-wf-T-base,
bag-size_wf,
nat_wf,
es-is-filter-image,
uiff_wf,
bool_cases,
assert_of_bnot,
not_wf,
less_than_wf
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[T:Type]. \mforall{}[X:EClass(T \mtimes{} \mBbbB{})]. \mforall{}[e:E].
uiff(\muparrow{}e \mmember{}\msubb{} Tagged\_tt(X);(\muparrow{}e \mmember{}\msubb{} X) \mwedge{} (\muparrow{}(snd(X(e)))))
Date html generated:
2015_07_20-PM-03_15_38
Last ObjectModification:
2015_01_27-PM-10_36_09
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