Nuprl Lemma : fpf-join-list-ap-disjoint
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[L:a:A fp-> B[a] List]. ∀[x:A].
(∀[f:a:A fp-> B[a]]. (⊕(L)(x) = f(x) ∈ B[x]) supposing ((↑x ∈ dom(f)) and (f ∈ L))) supposing
((∀f,g∈L. ∀x:A. (¬((↑x ∈ dom(f)) ∧ (↑x ∈ dom(g))))) and
(↑x ∈ dom(⊕(L))))
Proof
Definitions occuring in Statement :
fpf-join-list: ⊕(L),
fpf-ap: f(x),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
pairwise: (∀x,y∈L. P[x; y]),
l_member: (x ∈ l),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
not: ¬A,
and: P ∧ Q,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
fpf-join-list-ap,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
l_member_wf,
fpf_wf,
pairwise_wf2,
all_wf,
not_wf,
fpf-join-list_wf,
subtype_rel_list,
list_wf,
equal_wf,
fpf-ap_wf,
decidable__lt,
deq_wf,
true_wf,
squash_wf,
assert_functionality_wrt_uiff,
length_wf,
lelt_wf,
le_weakening,
less_than_transitivity2,
sq_stable__le,
less_than_wf,
le_wf,
select_wf
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[L:a:A fp-> B[a] List]. \mforall{}[x:A].
(\mforall{}[f:a:A fp-> B[a]]. (\moplus{}(L)(x) = f(x)) supposing ((\muparrow{}x \mmember{} dom(f)) and (f \mmember{} L))) supposing
((\mforall{}f,g\mmember{}L. \mforall{}x:A. (\mneg{}((\muparrow{}x \mmember{} dom(f)) \mwedge{} (\muparrow{}x \mmember{} dom(g))))) and
(\muparrow{}x \mmember{} dom(\moplus{}(L))))
Date html generated:
2015_07_17-AM-09_21_17
Last ObjectModification:
2015_07_16-AM-09_51_28
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