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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
in-eclass: e ∈b X,
latest-pair: (X&Y),
eclass-compose4: eclass-compose4(f;X;Y;Z;V),
member: t ∈ T,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
assert: ↑b,
top: Top,
eq_int: (i =z j),
iff: P ⇐⇒ Q,
or: P ∨ Q,
cand: A c∧ B,
true: True,
prop: ℙ,
rev_implies: P ⇐ Q,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
false: False,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
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:
2016_05_17-AM-07_14_20
Last ObjectModification:
2015_12_29-AM-00_09_20
Theory : event-ordering
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