Nuprl Lemma : is-interface-or
∀[Info:Type]. ∀es:EO+(Info). ∀X,Y:EClass(Top). ∀e:E. (↑e ∈b (X | Y) ⇐⇒ (↑e ∈b X) ∨ (↑e ∈b Y))
Proof
Definitions occuring in Statement :
es-interface-or: (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],
top: Top,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
universe: Type
Definitions unfolded in proof :
in-eclass: e ∈b X,
es-interface-or: (X | Y),
eclass: EClass(A[eo; e]),
oob-apply: oob-apply(xs;ys),
eclass-compose2: eclass-compose2(f;X;Y),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
nat: ℕ,
ifthenelse: if b then t else f fi ,
assert: ↑b,
top: Top,
eq_int: (i =z j),
iff: P ⇐⇒ Q,
or: P ∨ Q,
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
Latex:
\mforall{}[Info:Type]. \mforall{}es:EO+(Info). \mforall{}X,Y:EClass(Top). \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:
2016_05_16-PM-10_41_23
Last ObjectModification:
2015_12_29-AM-10_54_07
Theory : event-ordering
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