Nuprl Lemma : es-interface-conditional-domain-iff
∀[Info:Type]. ∀es:EO+(Info). ∀[A:Type]. ∀X,Y:EClass(A). ∀e:E. (↑e ∈b [X?Y] ⇐⇒ (↑e ∈b X) ∨ (↑e ∈b Y))
Proof
Definitions occuring in Statement :
cond-class: [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 :
es-E_wf,
event-ordering+_subtype,
eclass_wf,
event-ordering+_wf,
assert_functionality_wrt_uiff,
in-eclass_wf,
cond-class_wf,
top_wf,
es-interface-subtype_rel2,
bor_wf,
es-interface-conditional-domain,
assert_wf,
iff_wf,
or_wf,
assert_of_bor
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}[A:Type]. \mforall{}X,Y:EClass(A). \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_17-PM-00_51_26
Last ObjectModification:
2015_01_27-PM-11_01_03
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