Nuprl Lemma : lnk-decl-compatible-single
∀[l:IdLnk]. ∀[dt:tg:Id fp-> Type]. ∀[knd:Knd]. ∀[T:Type].
lnk-decl(l;dt) || knd : T
supposing (↑isrcv(knd)) ⇒ (↑lnk(knd) = l) ⇒ (↑tag(knd) ∈ dom(dt)) ⇒ (T = dt(tag(knd)) ∈ Type)
Proof
Definitions occuring in Statement :
lnk-decl: lnk-decl(l;dt),
fpf-single: x : v,
fpf-compatible: f || g,
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
Kind-deq: KindDeq,
eq_lnk: a = b,
tagof: tag(k),
lnk: lnk(k),
isrcv: isrcv(k),
Knd: Knd,
IdLnk: IdLnk,
id-deq: IdDeq,
Id: Id,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
fpf-compatible: f || g,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
top: Top,
uiff: uiff(P;Q),
Knd: Knd,
so_lambda: λ2x.t[x],
so_apply: x[s],
IdLnk: IdLnk,
Id: Id,
sq_type: SQType(T),
guard: {T},
prop: ℙ,
subtype_rel: A ⊆r B,
lnk-decl: lnk-decl(l;dt),
fpf-ap: f(x),
pi2: snd(t),
tagof: tag(k),
fpf-dom: x ∈ dom(f),
pi1: fst(t),
fpf: a:A fp-> B[a],
iff: P ⇐⇒ Q,
exists: ∃x:A. B[x],
rcv: rcv(l,tg),
isrcv: isrcv(k),
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
lnk: lnk(k),
outl: outl(x),
rev_uimplies: rev_uimplies(P;Q),
rev_implies: P ⇐ Q
Latex:
\mforall{}[l:IdLnk]. \mforall{}[dt:tg:Id fp-> Type]. \mforall{}[knd:Knd]. \mforall{}[T:Type].
lnk-decl(l;dt) || knd : T
supposing (\muparrow{}isrcv(knd)) {}\mRightarrow{} (\muparrow{}lnk(knd) = l) {}\mRightarrow{} (\muparrow{}tag(knd) \mmember{} dom(dt)) {}\mRightarrow{} (T = dt(tag(knd)))
Date html generated:
2016_05_16-AM-11_35_54
Last ObjectModification:
2015_12_29-AM-09_30_56
Theory : event-ordering
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