Nuprl Lemma : fpf-normalize-dom
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[g:x:A fp-> B[x]]. ∀[x:A]. (x ∈ dom(fpf-normalize(eq;g)) ~ x ∈ dom(g))
Proof
Definitions occuring in Statement :
fpf-normalize: fpf-normalize(eq;g),
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ─→ B[x],
universe: Type,
sqequal: s ~ t
Lemmas :
list_ind_cons_lemma,
list_ind_nil_lemma,
deq_member_cons_lemma,
deq_member_nil_lemma,
top_wf,
fpf_wf,
deq_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
equal-wf-T-base,
colength_wf_list,
list_wf,
list-cases,
reduce_nil_lemma,
product_subtype_list,
spread_cons_lemma,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
nat_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-commutes,
le_wf,
subtract_wf,
not-ge-2,
less-iff-le,
minus-minus,
add-swap,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
reduce_cons_lemma,
bool_wf,
uiff_transitivity,
assert_wf,
equal_wf,
eqtt_to_assert,
safe-assert-deq,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
bool_subtype_base,
iff_imp_equal_bool,
deq-member_wf,
filter_wf5,
l_member_wf,
bor_wf,
bfalse_wf,
member_filter_2,
eqof_wf,
member_filter,
or_wf,
assert_of_bor,
or_false_r,
assert-deq-member,
iff_wf
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[g:x:A fp-> B[x]]. \mforall{}[x:A].
(x \mmember{} dom(fpf-normalize(eq;g)) \msim{} x \mmember{} dom(g))
Date html generated:
2015_07_17-AM-11_16_48
Last ObjectModification:
2015_01_28-AM-07_37_45
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