Nuprl Lemma : is-or-latest
∀[Info,A,B:Type]. ∀es:EO+(Info). ∀X:EClass(A). ∀Y:EClass(B). ∀e:E. (↑e ∈b (X |- Y) ⇐⇒ (↑e ∈b X) ∨ (↑e ∈b Y))
Proof
Definitions occuring in Statement :
es-or-latest: (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
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
es-or-latest: (X |- Y),
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,
assert: ↑b,
ifthenelse: if b then t else f fi ,
iff: P ⇐⇒ Q,
or: P ∨ Q,
true: True,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
top: Top,
rev_implies: P ⇐ Q,
guard: {T},
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
bnot: ¬bb,
false: False
Latex:
\mforall{}[Info,A,B:Type].
\mforall{}es:EO+(Info). \mforall{}X:EClass(A). \mforall{}Y:EClass(B). \mforall{}e:E. (\muparrow{}e \mmember{}\msubb{} (X |\msupminus{} Y) \mLeftarrow{}{}\mRightarrow{} (\muparrow{}e \mmember{}\msubb{} X) \mvee{} (\muparrow{}e \mmember{}\msubb{} Y))
Date html generated:
2016_05_17-AM-07_15_15
Last ObjectModification:
2015_12_29-AM-00_04_17
Theory : event-ordering
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