Nuprl Lemma : fpf-union_wf
∀[A:Type]. ∀[B:A ─→ Type]. ∀[eq:EqDecider(A)]. ∀[f,g:x:A fp-> B[x] List]. ∀[x:A]. ∀[R:∩a:A. ((B[a] List) ─→ B[a] ─→ 𝔹)].
(fpf-union(f;g;eq;R;x) ∈ B[x] List)
Proof
Definitions occuring in Statement :
fpf-union: fpf-union(f;g;eq;R;x),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
isect: ∩x:A. B[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
list_wf,
bool_wf,
eqtt_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
append_wf,
fpf-ap_wf,
filter_wf5,
subtype_rel_dep_function,
l_member_wf,
subtype_rel_self,
set_wf,
eqff_to_assert,
assert-bnot,
assert_of_band,
assert_elim,
and_wf,
band_wf,
not_assert_elim,
btrue_neq_bfalse,
assert_wf,
nil_wf,
fpf_wf,
deq_wf
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:x:A fp-> B[x] List]. \mforall{}[x:A]. \mforall{}[R:\mcap{}a:A
((B[a] List)
{}\mrightarrow{} B[a]
{}\mrightarrow{} \mBbbB{})].
(fpf-union(f;g;eq;R;x) \mmember{} B[x] List)
Date html generated:
2015_07_17-AM-09_16_40
Last ObjectModification:
2015_01_28-AM-07_52_49
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