Nuprl Lemma : or-latest-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[e:E].
(X |- Y)(e) = ((X)- | (Y)-)(e) ∈ one_or_both(A;B) supposing (↑e ∈b (X |- Y)) ∧ Singlevalued(X) ∧ Singlevalued(Y)
Proof
Definitions occuring in Statement :
es-or-latest: (X |- Y),
es-latest-val: (X)-,
es-interface-or: (X | Y),
sv-class: Singlevalued(X),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
universe: Type,
equal: s = t ∈ T,
one_or_both: one_or_both(A;B)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
es-interface-or: (X | Y),
eclass-val: X(e),
es-or-latest: (X |- Y),
es-interface-union: X+Y,
es-latest-val: (X)-,
eclass-compose2: eclass-compose2(f;X;Y),
latest-pair: (X&Y),
eclass-compose4: eclass-compose4(f;X;Y;Z;V),
oob-apply: oob-apply(xs;ys),
in-eclass: e ∈b X,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
top: Top,
eq_int: (i =z j),
oobboth: oobboth(bval),
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
oobleft: oobleft(lval),
squash: ↓T,
true: True,
rev_implies: P ⇐ Q,
not: ¬A,
oobright: oobright(rval)
Latex:
\mforall{}[Info:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[e:E].
(X |\msupminus{} Y)(e) = ((X)\msupminus{} | (Y)\msupminus{})(e) supposing (\muparrow{}e \mmember{}\msubb{} (X |\msupminus{} Y)) \mwedge{} Singlevalued(X) \mwedge{} Singlevalued(Y)
Date html generated:
2016_05_17-AM-08_11_20
Last ObjectModification:
2016_01_17-PM-03_06_20
Theory : event-ordering
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