Nuprl Lemma : bag-moebius_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[b:bag(T)]. (bag-moebius(eq;b) ∈ ℤ)
Proof
Definitions occuring in Statement :
bag-moebius: bag-moebius(eq;b),
bag: bag(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-moebius: bag-moebius(eq;b),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
subtype_rel: A ⊆r B,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
sq_type: SQType(T),
guard: {T},
false: False,
prop: ℙ,
bfalse: ff,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
bag-has-no-repeats_wf,
bool_wf,
eqtt_to_assert,
eq_int_wf,
bag-size_wf,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
assert_of_eq_int,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
equal_wf,
bag_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
because_Cache,
productElimination,
independent_isectElimination,
remainderEquality,
applyEquality,
natural_numberEquality,
addLevel,
instantiate,
intEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
baseClosed,
independent_pairFormation,
impliesFunctionality,
minusEquality,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[b:bag(T)]. (bag-moebius(eq;b) \mmember{} \mBbbZ{})
Date html generated:
2018_05_21-PM-09_53_39
Last ObjectModification:
2017_07_26-PM-06_32_22
Theory : bags_2
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