Nuprl Lemma : es-is-interface-union
∀[Info:Type]. ∀es:EO+(Info). ∀[A,B:Type]. ∀X:EClass(A). ∀Y:EClass(B). ∀e:E. (↑e ∈b X+Y ⇐⇒ (↑e ∈b X) ∨ (↑e ∈b Y))
Proof
Definitions occuring in Statement :
es-interface-union: 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],
in-eclass: e ∈b X,
es-interface-union: X+Y,
eclass-compose2: eclass-compose2(f;X;Y),
member: t ∈ T,
eclass: EClass(A[eo; e]),
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,
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,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A,B:Type]. \mforall{}X:EClass(A). \mforall{}Y:EClass(B). \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_36_02
Last ObjectModification:
2015_12_29-AM-10_58_40
Theory : event-ordering
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