Nuprl Lemma : bag-count_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x:T]. ∀[bs:bag(T)]. ((#x in bs) ∈ ℕ)
Proof
Definitions occuring in Statement :
bag-count: (#x in bs),
bag: bag(T),
deq: EqDecider(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
bag: bag(T),
member: t ∈ T,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bag-count: (#x in bs),
so_lambda: λ2x.t[x],
deq: EqDecider(T),
so_apply: x[s],
uimplies: b supposing a,
nat: ℕ,
sq_type: SQType(T),
guard: {T},
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
squash: ↓T,
true: True,
ge: i ≥ j ,
count: count(P;L),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
eqof: eqof(d),
ifthenelse: if b then t else f fi ,
le: A ≤ B,
less_than': less_than'(a;b),
bfalse: ff,
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
nat_wf,
list_wf,
permutation-invariant,
equal_wf,
count_wf,
subtype_base_sq,
set_subtype_base,
le_wf,
int_subtype_base,
cons_wf,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
intformimplies_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formual_prop_imp_lemma,
iff_weakening_equal,
int_formula_prop_wf,
decidable__le,
nat_properties,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
permutation_wf,
equal-wf-base,
bag_wf,
deq_wf,
count-append,
nil_wf,
count-single,
reduce_cons_lemma,
bool_wf,
eqtt_to_assert,
safe-assert-deq,
itermAdd_wf,
int_term_value_add_lemma,
add_nat_wf,
false_wf,
add-is-int-iff,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
ifthenelse_wf
Rules used in proof :
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
pointwiseFunctionalityForEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
thin,
equalityTransitivity,
equalitySymmetry,
isectElimination,
cumulativity,
hypothesisEquality,
lambdaFormation,
because_Cache,
rename,
lambdaEquality,
applyEquality,
setElimination,
independent_functionElimination,
instantiate,
independent_isectElimination,
intEquality,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
imageElimination,
equalityUniverse,
levelHypothesis,
imageMemberEquality,
baseClosed,
universeEquality,
computeAll,
dependent_set_memberEquality,
applyLambdaEquality,
productEquality,
isect_memberFormation,
axiomEquality,
equalityElimination,
addEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x:T]. \mforall{}[bs:bag(T)]. ((\#x in bs) \mmember{} \mBbbN{})
Date html generated:
2018_05_21-PM-09_45_48
Last ObjectModification:
2017_07_26-PM-06_29_52
Theory : bags_2
Home
Index