Nuprl Lemma : fpf-join-wf
∀[A:Type]. ∀[B,C,D:A ─→ Type]. ∀[f:a:A fp-> B[a]]. ∀[g:a:A fp-> C[a]]. ∀[eq:EqDecider(A)].
(f ⊕ g ∈ a:A fp-> D[a]) supposing
((∀a:A. ((↑a ∈ dom(g)) ⇒ (C[a] ⊆r D[a]))) and
(∀a:A. ((↑a ∈ dom(f)) ⇒ (B[a] ⊆r D[a]))))
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
assert: ↑b,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
function: x:A ─→ B[x],
universe: Type
Lemmas :
fpf_ap_pair_lemma,
append_wf,
filter_wf5,
l_member_wf,
bnot_wf,
deq-member_wf,
bool_wf,
eqtt_to_assert,
assert-deq-member,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
member_append,
member_filter,
assert_wf,
or_wf,
all_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
subtype_rel_wf,
deq_wf,
fpf_wf
\mforall{}[A:Type]. \mforall{}[B,C,D:A {}\mrightarrow{} Type]. \mforall{}[f:a:A fp-> B[a]]. \mforall{}[g:a:A fp-> C[a]]. \mforall{}[eq:EqDecider(A)].
(f \moplus{} g \mmember{} a:A fp-> D[a]) supposing
((\mforall{}a:A. ((\muparrow{}a \mmember{} dom(g)) {}\mRightarrow{} (C[a] \msubseteq{}r D[a]))) and
(\mforall{}a:A. ((\muparrow{}a \mmember{} dom(f)) {}\mRightarrow{} (B[a] \msubseteq{}r D[a]))))
Date html generated:
2015_07_17-AM-09_19_01
Last ObjectModification:
2015_01_28-AM-07_58_34
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