Nuprl Lemma : es-dt-dom
∀[l:IdLnk]. ∀[da:k:Knd fp-> Type]. ∀[tg:Id]. uiff(↑tg ∈ dom(dt(l;da));↑rcv(l,tg) ∈ dom(da))
Proof
Definitions occuring in Statement :
es-dt: dt(l;da),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
Kind-deq: KindDeq,
rcv: rcv(l,tg),
Knd: Knd,
IdLnk: IdLnk,
id-deq: IdDeq,
Id: Id,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
uimplies: b supposing a,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
es-dt: dt(l;da),
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
not: ¬A,
top: Top,
isl: isl(x),
outl: outl(x),
cand: A c∧ B,
squash: ↓T,
true: True,
lnk: lnk(k),
isrcv: isrcv(k),
tagof: tag(k),
rcv: rcv(l,tg),
Knd: Knd,
pi1: fst(t),
pi2: snd(t)
Latex:
\mforall{}[l:IdLnk]. \mforall{}[da:k:Knd fp-> Type]. \mforall{}[tg:Id]. uiff(\muparrow{}tg \mmember{} dom(dt(l;da));\muparrow{}rcv(l,tg) \mmember{} dom(da))
Date html generated:
2016_05_16-AM-11_39_48
Last ObjectModification:
2016_01_17-PM-03_52_17
Theory : event-ordering
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