Nuprl Lemma : is-latest-pair
∀[Info,A,B:Type].
∀X:EClass(A). ∀Y:EClass(B). ∀es:EO+(Info). ∀e:E.
(↑e ∈b (X&Y) ⇐⇒ ((↑e ∈b X) ∧ ((↑e ∈b Y) ∨ (↑e ∈b Prior(Y)))) ∨ ((↑e ∈b Y) ∧ ((↑e ∈b X) ∨ (↑e ∈b Prior(X)))))
Proof
Definitions occuring in Statement :
latest-pair: (X&Y),
primed-class: Prior(X),
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,
and: P ∧ Q,
universe: Type
Lemmas :
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
top_wf,
bool_wf,
eqtt_to_assert,
bag_size_single_lemma,
assert_wf,
primed-class_wf,
or_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
false_wf,
true_wf,
bag_size_empty_lemma,
event-ordering+_wf,
eclass_wf
Latex:
\mforall{}[Info,A,B:Type].
\mforall{}X:EClass(A). \mforall{}Y:EClass(B). \mforall{}es:EO+(Info). \mforall{}e:E.
(\muparrow{}e \mmember{}\msubb{} (X\&Y)
\mLeftarrow{}{}\mRightarrow{} ((\muparrow{}e \mmember{}\msubb{} X) \mwedge{} ((\muparrow{}e \mmember{}\msubb{} Y) \mvee{} (\muparrow{}e \mmember{}\msubb{} Prior(Y)))) \mvee{} ((\muparrow{}e \mmember{}\msubb{} Y) \mwedge{} ((\muparrow{}e \mmember{}\msubb{} X) \mvee{} (\muparrow{}e \mmember{}\msubb{} Prior(X)))))
Date html generated:
2015_07_21-PM-03_45_44
Last ObjectModification:
2015_01_27-PM-06_32_53
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