Nuprl Lemma : fpf-join-list-dom
∀[A:Type]. ∀eq:EqDecider(A). ∀[B:A ─→ Type]. ∀L:a:A fp-> B[a] List. ∀x:A. (↑x ∈ dom(⊕(L)) ⇐⇒ (∃f∈L. ↑x ∈ dom(f)))
Proof
Definitions occuring in Statement :
fpf-join-list: ⊕(L),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
l_exists: (∃x∈L. P[x]),
list: T List,
assert: ↑b,
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 :
list_induction,
all_wf,
iff_wf,
assert_wf,
fpf-dom_wf,
fpf-join-list_wf,
top_wf,
subtype_rel_list,
fpf_wf,
subtype-fpf2,
subtype_top,
l_exists_wf,
l_member_wf,
list_wf,
deq_wf,
reduce_nil_lemma,
deq_member_nil_lemma,
false_wf,
l_exists_nil,
l_exists_wf_nil,
l_exists_cons,
cons_wf,
or_wf,
reduce_cons_lemma,
fpf-join-dom,
fpf-join_wf
\mforall{}[A:Type]
\mforall{}eq:EqDecider(A)
\mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}L:a:A fp-> B[a] List. \mforall{}x:A. (\muparrow{}x \mmember{} dom(\moplus{}(L)) \mLeftarrow{}{}\mRightarrow{} (\mexists{}f\mmember{}L. \muparrow{}x \mmember{} dom(f)))
Date html generated:
2015_07_17-AM-09_20_50
Last ObjectModification:
2015_01_28-AM-07_49_20
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