Nuprl Lemma : bag-eq_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:bag(T)]. (bag-eq(eq;as;bs) ∈ 𝔹)
Proof
Definitions occuring in Statement :
bag-eq: bag-eq(eq;as;bs),
bag: bag(T),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-eq: bag-eq(eq;as;bs),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
band_wf,
bag-all_wf,
eq_int_wf,
bag-count_wf,
nat_wf,
lt_int_wf,
bag_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
hypothesis,
applyEquality,
setElimination,
rename,
because_Cache,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as,bs:bag(T)]. (bag-eq(eq;as;bs) \mmember{} \mBbbB{})
Date html generated:
2016_05_15-PM-08_00_22
Last ObjectModification:
2015_12_27-PM-04_16_00
Theory : bags_2
Home
Index