Nuprl Lemma : fpf-join-list-domain
∀[A:Type]
∀eq:EqDecider(A)
∀[B:A ─→ Type]. ∀L:a:A fp-> B[a] List. ∀x:A. ((x ∈ fpf-domain(⊕(L))) ⇐⇒ (∃f∈L. (x ∈ fpf-domain(f))))
Proof
Definitions occuring in Statement :
fpf-join-list: ⊕(L),
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
l_exists: (∃x∈L. P[x]),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
fpf-join-list-dom,
member-fpf-domain,
fpf-join-list_wf,
top_wf,
subtype_rel_list,
fpf_wf,
subtype-fpf2,
subtype_top,
l_exists_functionality,
l_member_wf,
assert_wf,
fpf-dom_wf,
fpf-domain_wf,
set_wf,
l_exists_wf,
list_wf,
deq_wf
\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))) \mLeftarrow{}{}\mRightarrow{} (\mexists{}f\mmember{}L. (x \mmember{} fpf-domain(f))))
Date html generated:
2015_07_17-AM-09_20_55
Last ObjectModification:
2015_01_28-AM-07_47_26
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