Nuprl Lemma : bag-size_wf
∀[C:Type]. ∀[bs:bag(C)].  (#(bs) ∈ ℕ)
Proof
Definitions occuring in Statement : 
bag-size: #(bs)
, 
bag: bag(T)
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
bag: bag(T)
, 
quotient: x,y:A//B[x; y]
, 
and: P ∧ Q
, 
bag-size: #(bs)
, 
prop: ℙ
, 
nat: ℕ
, 
uimplies: b supposing a
, 
ge: i ≥ j 
, 
all: ∀x:A. B[x]
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
le: A ≤ B
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
top: Top
Lemmas referenced : 
le_wf, 
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, 
non_neg_length, 
permutation-length, 
bag_wf, 
permutation_wf, 
list_wf, 
equal-wf-base, 
nat_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalHypSubstitution, 
pointwiseFunctionalityForEquality, 
lemma_by_obid, 
hypothesis, 
sqequalRule, 
pertypeElimination, 
productElimination, 
thin, 
productEquality, 
isectElimination, 
hypothesisEquality, 
because_Cache, 
cumulativity, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
universeEquality, 
dependent_set_memberEquality, 
independent_isectElimination, 
dependent_functionElimination, 
unionElimination, 
natural_numberEquality, 
dependent_pairFormation, 
lambdaEquality, 
int_eqEquality, 
intEquality, 
voidElimination, 
voidEquality, 
independent_pairFormation, 
computeAll
Latex:
\mforall{}[C:Type].  \mforall{}[bs:bag(C)].    (\#(bs)  \mmember{}  \mBbbN{})
Date html generated:
2016_05_15-PM-02_24_49
Last ObjectModification:
2016_01_16-AM-08_57_24
Theory : bags
Home
Index