Nuprl Lemma : bag-subtype-list
∀T:Type. (bag(T) ⊆r (Top List))
Proof
Definitions occuring in Statement : 
bag: bag(T)
, 
list: T List
, 
subtype_rel: A ⊆r B
, 
top: Top
, 
all: ∀x:A. B[x]
, 
universe: Type
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
bag: bag(T)
, 
quotient: x,y:A//B[x; y]
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
uimplies: b supposing a
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
top: Top
, 
so_apply: x[s]
, 
ge: i ≥ j 
, 
le: A ≤ B
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
not: ¬A
, 
squash: ↓T
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
uiff: uiff(P;Q)
, 
true: True
Lemmas referenced : 
bag_wf, 
list_wf, 
top_wf, 
permutation-length, 
permutation_wf, 
equal_wf, 
equal-wf-base, 
list_induction, 
all_wf, 
length_wf, 
subtype_rel_list, 
equal-wf-base-T, 
length_of_nil_lemma, 
nil_wf, 
length_of_cons_lemma, 
non_neg_length, 
satisfiable-full-omega-tt, 
intformand_wf, 
intformle_wf, 
itermConstant_wf, 
itermVar_wf, 
intformeq_wf, 
itermAdd_wf, 
int_formula_prop_and_lemma, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_formula_prop_eq_lemma, 
int_term_value_add_lemma, 
int_formula_prop_wf, 
cons_wf, 
equal-wf-T-base, 
squash_wf, 
true_wf, 
decidable__equal_int, 
add-is-int-iff, 
intformnot_wf, 
int_formula_prop_not_lemma, 
false_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
lambdaEquality, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
cumulativity, 
hypothesisEquality, 
hypothesis, 
universeEquality, 
pointwiseFunctionalityForEquality, 
sqequalRule, 
pertypeElimination, 
productElimination, 
equalityTransitivity, 
equalitySymmetry, 
because_Cache, 
rename, 
independent_isectElimination, 
dependent_functionElimination, 
independent_functionElimination, 
productEquality, 
functionEquality, 
intEquality, 
applyEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
baseClosed, 
natural_numberEquality, 
dependent_pairFormation, 
int_eqEquality, 
independent_pairFormation, 
computeAll, 
addEquality, 
imageElimination, 
unionElimination, 
pointwiseFunctionality, 
promote_hyp, 
baseApply, 
closedConclusion, 
imageMemberEquality
Latex:
\mforall{}T:Type.  (bag(T)  \msubseteq{}r  (Top  List))
Date html generated:
2017_10_01-AM-08_44_52
Last ObjectModification:
2017_07_26-PM-04_30_23
Theory : bags
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