Nuprl Lemma : bag-size-zero
∀[C:Type]. ∀[bs:bag(C)]. bs ~ {} supposing #(bs) ≤ 0
Proof
Definitions occuring in Statement :
bag-size: #(bs),
empty-bag: {},
bag: bag(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bag-size: #(bs),
or: P ∨ Q,
empty-bag: {},
uimplies: b supposing a,
prop: ℙ,
cons: [a / b],
top: Top,
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
nat: ℕ
Lemmas referenced :
bag-subtype-list,
list_wf,
top_wf,
list-cases,
length_of_nil_lemma,
le_wf,
product_subtype_list,
length_of_cons_lemma,
non_neg_length,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
length_wf,
equal_wf,
bag_wf,
bag-size_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
sqequalRule,
isectElimination,
lambdaFormation,
unionElimination,
sqequalAxiom,
natural_numberEquality,
promote_hyp,
hypothesis_subsumption,
productElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
addEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
because_Cache,
cumulativity,
setElimination,
rename,
universeEquality
Latex:
\mforall{}[C:Type]. \mforall{}[bs:bag(C)]. bs \msim{} \{\} supposing \#(bs) \mleq{} 0
Date html generated:
2017_10_01-AM-08_45_49
Last ObjectModification:
2017_07_26-PM-04_30_56
Theory : bags
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