Nuprl Lemma : es-prior-class-when-programmable
∀[Info,A,B:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[d:A].
(X'?d) when Y
= eclass-compose2(λys,xs. if (#(ys) =z 1)
then if (#(xs) =z 1) then {<only(ys), only(xs)>} else {<only(ys), d>} fi
else {}
fi ;Y;Prior(X))
∈ EClass(B × A)
supposing Singlevalued(X)
Proof
Definitions occuring in Statement :
es-prior-class-when: (X'?d) when Y,
primed-class: Prior(X),
eclass-compose2: eclass-compose2(f;X;Y),
sv-class: Singlevalued(X),
eclass: EClass(A[eo; e]),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
pair: <a, b>,
product: x:A × B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T,
bag-only: only(bs),
bag-size: #(bs),
single-bag: {x},
empty-bag: {}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
nat: ℕ,
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,
top: Top,
prop: ℙ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
sv-class: Singlevalued(X),
eclass-compose2: eclass-compose2(f;X;Y),
eclass-val: X(e),
in-eclass: e ∈b X,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
le: A ≤ B,
less_than': less_than'(a;b),
es-prior-class-when: (X'?d) when Y,
iff: P ⇐⇒ Q,
eq_int: (i =z j),
true: True,
rev_implies: P ⇐ Q,
squash: ↓T
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)]. \mforall{}[d:A].
(X'?d) when Y
= eclass-compose2(\mlambda{}ys,xs. if (\#(ys) =\msubz{} 1)
then if (\#(xs) =\msubz{} 1) then \{<only(ys), only(xs)>\} else \{<only(ys), d>\} fi
else \{\}
fi ;Y;Prior(X))
supposing Singlevalued(X)
Date html generated:
2016_05_17-AM-08_11_39
Last ObjectModification:
2016_01_17-PM-02_40_33
Theory : event-ordering
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