Nuprl Lemma : until-class-simple-comb
∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[Y:EClass(Top)].
((X until Y) = λxs,ys.if bag-null(ys) then xs else {} fi |X;Prior(Y)| ∈ EClass(A))
Proof
Definitions occuring in Statement :
simple-comb2: λx,y.F[x; y]|X;Y|,
primed-class: Prior(X),
until-class: (X until Y),
eclass: EClass(A[eo; e]),
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
equal: s = t ∈ T,
bag-null: bag-null(bs),
empty-bag: {}
Definitions unfolded in proof :
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
simple-comb2: λx,y.F[x; y]|X;Y|,
until-class: (X until Y),
simple-comb: simple-comb(F;Xs),
select: L[n],
cons: [a / b],
subtract: n - m,
all: ∀x:A. B[x],
or: P ∨ Q,
existse-before: ∃e<e'.P[e],
exists: ∃x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
squash: ↓T,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
not: ¬A,
false: False,
bfalse: ff,
iff: P ⇐⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_uimplies: rev_uimplies(P;Q),
alle-lt: ∀e<e'.P[e],
top: Top,
guard: {T}
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(Top)].
((X until Y) = \mlambda{}xs,ys.if bag-null(ys) then xs else \{\} fi |X;Prior(Y)|)
Date html generated:
2016_05_17-AM-06_32_34
Last ObjectModification:
2016_01_17-PM-06_37_32
Theory : event-ordering
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