Nuprl Lemma : fpf-join-is-empty
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[f,g:x:A fp-> Top]. (fpf-is-empty(f ⊕ g) ~ fpf-is-empty(f) ∧b fpf-is-empty(g))
Proof
Definitions occuring in Statement :
fpf-join: f ⊕ g,
fpf-is-empty: fpf-is-empty(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
band: p ∧b q,
uall: ∀[x:A]. B[x],
top: Top,
universe: Type,
sqequal: s ~ t
Lemmas :
subtype_base_sq,
bool_wf,
bool_subtype_base,
fpf_wf,
top_wf,
deq_wf,
list-cases,
list_ind_nil_lemma,
deq_member_nil_lemma,
length_of_nil_lemma,
product_subtype_list,
list_ind_cons_lemma,
deq_member_cons_lemma,
length_of_cons_lemma,
filter_trivial,
btrue_wf,
eq_int_wf,
length_wf,
int_seg_wf,
length-append,
filter_wf5,
l_member_wf,
bnot_wf,
bor_wf,
deq-member_wf,
eqtt_to_assert,
assert_of_eq_int,
non_neg_length,
length_wf_nat,
eqof_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
assert-bnot,
neg_assert_of_eq_int,
iff_imp_equal_bool,
equal-wf-T-base,
iff_transitivity,
assert_wf,
iff_weakening_uiff,
assert_of_band,
iff_wf
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[f,g:x:A fp-> Top].
(fpf-is-empty(f \moplus{} g) \msim{} fpf-is-empty(f) \mwedge{}\msubb{} fpf-is-empty(g))
Date html generated:
2015_07_17-AM-09_19_57
Last ObjectModification:
2015_01_28-AM-07_49_16
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