Nuprl Lemma : interface-or-val
∀[Info:Type]. ∀[es:EO+(Info)]. ∀[A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[e:E].
(X | Y)(e)
= if e ∈b X then if e ∈b Y then oobboth(<X(e), Y(e)>) else oobleft(X(e)) fi else oobright(Y(e)) fi
∈ one_or_both(A;B)
supposing ↑e ∈b (X | Y)
Proof
Definitions occuring in Statement :
es-interface-or: (X | Y),
eclass-val: X(e),
in-eclass: e ∈b X,
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
assert: ↑b,
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
pair: <a, b>,
universe: Type,
equal: s = t ∈ T,
oobright: oobright(rval),
oobleft: oobleft(lval),
oobboth: oobboth(bval),
one_or_both: one_or_both(A;B)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
eclass: EClass(A[eo; e]),
eclass-val: X(e),
in-eclass: e ∈b X,
es-interface-or: (X | Y),
oob-apply: oob-apply(xs;ys),
eclass-compose2: eclass-compose2(f;X;Y),
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
nat: ℕ,
ifthenelse: if b then t else f fi ,
top: Top,
eq_int: (i =z j),
assert: ↑b,
cand: A c∧ B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
prop: ℙ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
nequal: a ≠ b ∈ T ,
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].
(X | Y)(e)
= if e \mmember{}\msubb{} X then if e \mmember{}\msubb{} Y then oobboth(<X(e), Y(e)>) else oobleft(X(e)) fi else oobright(Y(e)) f\000Ci
supposing \muparrow{}e \mmember{}\msubb{} (X | Y)
Date html generated:
2016_05_16-PM-10_41_35
Last ObjectModification:
2016_01_17-PM-07_23_45
Theory : event-ordering
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