Nuprl Lemma : fpf-join-range
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[df:x:A fp-> Type]. ∀[f:x:A fp-> df(x)?Top]. ∀[dg:x:A fp-> Type].
∀[g:x:A fp-> dg(x)?Top].
(f ⊕ g ∈ x:A fp-> df ⊕ dg(x)?Top) supposing
((∀x:A. ((↑x ∈ dom(g)) ⇒ (↑x ∈ dom(dg)))) and
(∀x:A. ((↑x ∈ dom(f)) ⇒ (↑x ∈ dom(df)))) and
df || dg)
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-compatible: f || g,
fpf-cap: f(x)?z,
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
universe: Type
Lemmas :
all_wf,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
subtype_top,
fpf-cap_wf,
top_wf,
fpf-compatible_wf,
fpf_wf,
deq_wf,
append_wf,
filter_wf5,
l_member_wf,
bnot_wf,
deq-member_wf,
bool_wf,
equal-wf-T-base,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf-ap_wf,
fpf-join_wf,
subtype_rel_wf,
squash_wf,
true_wf,
fpf-join-ap,
iff_weakening_equal,
subtype_rel_self,
fpf-join-dom,
member_append,
assert-deq-member,
member_filter_2,
subtype_rel_weakening,
ext-eq_weakening
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[df:x:A fp-> Type]. \mforall{}[f:x:A fp-> df(x)?Top]. \mforall{}[dg:x:A fp-> Type].
\mforall{}[g:x:A fp-> dg(x)?Top].
(f \moplus{} g \mmember{} x:A fp-> df \moplus{} dg(x)?Top) supposing
((\mforall{}x:A. ((\muparrow{}x \mmember{} dom(g)) {}\mRightarrow{} (\muparrow{}x \mmember{} dom(dg)))) and
(\mforall{}x:A. ((\muparrow{}x \mmember{} dom(f)) {}\mRightarrow{} (\muparrow{}x \mmember{} dom(df)))) and
df || dg)
Date html generated:
2015_07_17-AM-09_20_26
Last ObjectModification:
2015_02_04-PM-05_07_44
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