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
Lemmas :
assert-deq-member,
Knd_wf,
Kind-deq_wf,
map_wf,
Id_wf,
rcv_wf,
member_map,
subtype_base_sq,
union_subtype_base,
IdLnk_wf,
product_subtype_base,
atom2_subtype_base,
assert-eq-lnk,
id-deq_wf
\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:
2015_07_17-AM-11_16_04
Last ObjectModification:
2015_01_28-AM-07_39_24
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