Nuprl Lemma : rec-bind-class_wf
∀[Info,A,B:Type]. ∀[X:A ─→ EClass(B)]. ∀[Y:A ─→ EClass(A)].
rec-bind-class(X;Y) ∈ A ─→ EClass(B) supposing not-self-starting{i:l}(Info;A;Y)
Proof
Definitions occuring in Statement :
rec-bind-class: rec-bind-class(X;Y),
not-self-starting: not-self-starting{i:l}(Info;A;Y),
eclass: EClass(A[eo; e]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ─→ B[x],
universe: Type
Lemmas :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
length_wf,
es-E_wf,
Id_wf,
es-loc_wf,
es-le-before_wf,
event-ordering+_wf,
event-ordering+_subtype,
decidable__le,
subtract_wf,
false_wf,
not-ge-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
nat_wf,
non_neg_length,
length_wf_nat,
void_wf,
not-self-starting_wf,
eclass_wf,
es-le-before_wf2,
list-subtype-bag,
es-le_wf,
bag_wf,
bag-append_wf,
bag-combine-member-wf,
bag-combine_wf,
eo-forward-le-before,
list-subtype,
l_member_wf,
squash_wf,
true_wf,
list_wf,
iff_weakening_equal,
member_filter_2,
subtype_rel_list,
es-ble_wf,
assert-es-ble,
member-es-le-before,
subtype_rel_sets,
eo-forward_wf,
member-eo-forward-E,
equal_wf,
sq_stable_from_decidable,
decidable__es-le,
eo-forward-le2,
equal-eo-forward-E,
es-le-self,
and_wf,
member_wf,
classrel_wf,
es-le_weakening,
length-filter,
le_wf,
length-filter-decreases,
l_exists_iff,
set_wf,
not_wf,
assert_wf,
eo-forward-loc,
es-le-loc,
es-locl_transitivity2,
es-locl_irreflexivity,
eo-forward-le,
decidable__lt,
filter_wf5,
eo-forward-E-subtype,
member-es-le-before2,
bag-member_wf
Latex:
\mforall{}[Info,A,B:Type]. \mforall{}[X:A {}\mrightarrow{} EClass(B)]. \mforall{}[Y:A {}\mrightarrow{} EClass(A)].
rec-bind-class(X;Y) \mmember{} A {}\mrightarrow{} EClass(B) supposing not-self-starting\{i:l\}(Info;A;Y)
Date html generated:
2015_07_21-PM-03_13_10
Last ObjectModification:
2015_02_04-PM-06_23_33
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