Nuprl Lemma : fpf-normalize-ap
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[g:x:A fp-> B[x]]. ∀[x:A].
fpf-normalize(eq;g)(x) = g(x) ∈ B[x] supposing ↑x ∈ dom(g)
Proof
Definitions occuring in Statement :
fpf-normalize: fpf-normalize(eq;g),
fpf-ap: f(x),
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],
so_apply: x[s],
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
list_ind_cons_lemma,
list_ind_nil_lemma,
fpf_ap_pair_lemma,
deq_member_cons_lemma,
deq_member_nil_lemma,
assert_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
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,
list-subtype,
l_member_wf,
deq-member_wf,
set_wf,
subtype_rel_list,
bool_wf,
uiff_transitivity,
equal_wf,
eqtt_to_assert,
safe-assert-deq,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
cons_wf,
member_wf,
subtype_rel_self,
subtype_rel_wf,
assert-deq-member,
cons_member
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[g:x:A fp-> B[x]]. \mforall{}[x:A].
fpf-normalize(eq;g)(x) = g(x) supposing \muparrow{}x \mmember{} dom(g)
Date html generated:
2015_07_17-AM-11_16_57
Last ObjectModification:
2015_01_28-AM-07_38_05
Home
Index