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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