Nuprl Lemma : bag-size-restrict
∀[T:Type]. ∀[b:bag(T)]. ∀[eq:EqDecider(T)]. ∀[x:T]. (#((b|x)) ~ (#x in b))
Proof
Definitions occuring in Statement :
bag-restrict: (b|x),
bag-count: (#x in bs),
bag-size: #(bs),
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
prop: ℙ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
bag-restrict: (b|x),
deq: EqDecider(T),
subtype_rel: A ⊆r B,
sq_type: SQType(T)
Lemmas referenced :
bag_wf,
deq_wf,
nat_wf,
bag-filter_wf,
assert_wf,
bag-count-sqequal,
int_formula_prop_wf,
int_formula_prop_not_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformnot_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
le_wf,
nat_properties,
bag-restrict_wf,
bag-size_wf,
decidable__le,
int_subtype_base,
set_subtype_base,
subtype_base_sq
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
sqequalRule,
hypothesis,
dependent_functionElimination,
unionElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
intEquality,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
dependent_set_memberEquality,
independent_functionElimination,
sqequalAxiom,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[b:bag(T)]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:T]. (\#((b|x)) \msim{} (\#x in b))
Date html generated:
2016_05_15-PM-08_10_20
Last ObjectModification:
2016_01_16-PM-01_27_22
Theory : bags_2
Home
Index