Nuprl Lemma : sub-bag-of-bag-rep
∀[T:Type]. ∀x:T. ∀n:ℕ. ∀[b:bag(T)]. b = bag-rep(#(b);x) ∈ bag(T) supposing sub-bag(T;b;bag-rep(n;x))
Proof
Definitions occuring in Statement :
sub-bag: sub-bag(T;as;bs),
bag-rep: bag-rep(n;x),
bag-size: #(bs),
bag: bag(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
single-valued-bag: single-valued-bag(b;T),
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bag-rep: bag-rep(n;x),
top: Top,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
and: P ∧ Q,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_weakening_equal,
true_wf,
squash_wf,
sv-bag-only_wf,
int_formula_prop_less_lemma,
intformless_wf,
le_wf,
decidable__lt,
bag-member-sv-bag-only,
single-valued-bag-is-rep,
empty-bag_wf,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermConstant_wf,
itermVar_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
bag-size-zero,
primrec0_lemma,
int_subtype_base,
subtype_base_sq,
bag_wf,
sub-bag_wf,
nat_wf,
bag-size_wf,
decidable__equal_int,
bag-member_wf,
member-bag-rep,
list-subtype-bag,
bag-rep_wf,
sub-bag-member
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
applyEquality,
independent_isectElimination,
lambdaEquality,
sqequalRule,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
setElimination,
rename,
natural_numberEquality,
unionElimination,
isect_memberEquality,
axiomEquality,
universeEquality,
instantiate,
cumulativity,
intEquality,
independent_functionElimination,
voidElimination,
voidEquality,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
setEquality,
imageElimination,
imageMemberEquality,
baseClosed,
productElimination
Latex:
\mforall{}[T:Type]. \mforall{}x:T. \mforall{}n:\mBbbN{}. \mforall{}[b:bag(T)]. b = bag-rep(\#(b);x) supposing sub-bag(T;b;bag-rep(n;x))
Date html generated:
2016_05_15-PM-02_46_28
Last ObjectModification:
2016_01_16-AM-08_44_01
Theory : bags
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