Nuprl Lemma : strict-bag-function_wf
∀[L:Type List]. ∀[B:Type]. ∀[G:tuple-type(map(λT.bag(T);L)) ⟶ bag(B)]. ∀[S:ℕ||L|| List].
  (strict-bag-function(G;L;B;S) ∈ ℙ)
Proof
Definitions occuring in Statement : 
strict-bag-function: strict-bag-function(G;L;B;S)
, 
bag: bag(T)
, 
tuple-type: tuple-type(L)
, 
length: ||as||
, 
map: map(f;as)
, 
list: T List
, 
int_seg: {i..j-}
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
lambda: λx.A[x]
, 
function: x:A ⟶ B[x]
, 
natural_number: $n
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
strict-bag-function: strict-bag-function(G;L;B;S)
, 
so_lambda: λ2x.t[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
uimplies: b supposing a
, 
guard: {T}
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
and: P ∧ Q
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
, 
top: Top
, 
less_than: a < b
, 
squash: ↓T
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
, 
cand: A c∧ B
Lemmas referenced : 
subtype_rel_self, 
top_wf, 
subtype_rel_list, 
select-map, 
map_length, 
map-length, 
int_seg_subtype_nat, 
select-tuple_wf, 
list_wf, 
equal-wf-T-base, 
empty-bag_wf, 
int_formula_prop_less_lemma, 
intformless_wf, 
decidable__lt, 
int_formula_prop_wf, 
int_term_value_var_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_and_lemma, 
itermVar_wf, 
itermConstant_wf, 
intformle_wf, 
intformnot_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
decidable__le, 
int_seg_properties, 
select_wf, 
equal_wf, 
l_member_wf, 
length_wf, 
int_seg_wf, 
l_all_wf, 
bag_wf, 
map_wf, 
tuple-type_wf, 
all_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
instantiate, 
universeEquality, 
because_Cache, 
lambdaEquality, 
cumulativity, 
hypothesisEquality, 
hypothesis, 
functionEquality, 
natural_numberEquality, 
lambdaFormation, 
setElimination, 
rename, 
independent_isectElimination, 
productElimination, 
dependent_functionElimination, 
unionElimination, 
dependent_pairFormation, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
independent_pairFormation, 
computeAll, 
imageElimination, 
setEquality, 
applyEquality, 
baseClosed, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}[L:Type  List].  \mforall{}[B:Type].  \mforall{}[G:tuple-type(map(\mlambda{}T.bag(T);L))  {}\mrightarrow{}  bag(B)].  \mforall{}[S:\mBbbN{}||L||  List].
    (strict-bag-function(G;L;B;S)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_15-PM-02_58_46
Last ObjectModification:
2016_01_16-AM-08_39_33
Theory : bags
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