Nuprl Lemma : fpf-join-list-ap2
∀[A:Type]
∀eq:EqDecider(A)
∀[B:A ─→ Type]
∀L:a:A fp-> B[a] List. ∀x:A. ((x ∈ fpf-domain(⊕(L))) ⇒ (∃f∈L. (↑x ∈ dom(f)) ∧ (⊕(L)(x) = f(x) ∈ B[x])))
Proof
Definitions occuring in Statement :
fpf-join-list: ⊕(L),
fpf-ap: f(x),
fpf-domain: fpf-domain(f),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
l_exists: (∃x∈L. P[x]),
l_member: (x ∈ l),
list: T List,
assert: ↑b,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
fpf-join-list-ap,
list_wf,
fpf_wf,
deq_wf,
l_member_wf,
fpf-domain_wf,
fpf-join-list_wf,
top_wf,
subtype_rel_list,
subtype-fpf2,
subtype_top,
member-fpf-domain
\mforall{}[A:Type]
\mforall{}eq:EqDecider(A)
\mforall{}[B:A {}\mrightarrow{} Type]
\mforall{}L:a:A fp-> B[a] List. \mforall{}x:A.
((x \mmember{} fpf-domain(\moplus{}(L))) {}\mRightarrow{} (\mexists{}f\mmember{}L. (\muparrow{}x \mmember{} dom(f)) \mwedge{} (\moplus{}(L)(x) = f(x))))
Date html generated:
2015_07_17-AM-09_21_13
Last ObjectModification:
2015_01_28-AM-07_46_54
Home
Index