Nuprl Lemma : es-is-interface-union
∀[Info:Type]. ∀es:EO+(Info). ∀[A,B:Type]. ∀X:EClass(A). ∀Y:EClass(B). ∀e:E. (↑e ∈b X+Y ⇐⇒ (↑e ∈b X) ∨ (↑e ∈b Y))
Proof
Definitions occuring in Statement :
es-interface-union: X+Y,
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
universe: Type
Lemmas :
eq_int_wf,
bag-size_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
nat_wf,
bag_size_single_lemma,
assert_wf,
true_wf,
or_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
bag_size_empty_lemma,
false_wf,
es-E_wf,
event-ordering+_subtype,
eclass_wf,
event-ordering+_wf
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A,B:Type]. \mforall{}X:EClass(A). \mforall{}Y:EClass(B). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} X+Y \mLeftarrow{}{}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} X) \mvee{} (\muparrow{}e \mmember{}\msubb{} Y))
Date html generated:
2015_07_20-PM-03_19_26
Last ObjectModification:
2015_01_27-PM-10_22_49
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