Nuprl Lemma : deq-sub-bag_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as,bs:bag(T)]. (deq-sub-bag(eq;as;bs) ∈ 𝔹)
Proof
Definitions occuring in Statement :
deq-sub-bag: deq-sub-bag(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 :
deq-sub-bag: deq-sub-bag(eq;as;bs),
member: t ∈ T,
uall: ∀[x:A]. B[x],
decidable__sub-bag,
deq-exists,
decidable_functionality,
iff_preserves_decidability,
sub-bag-iff,
decidable__assert,
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
or: P ∨ Q,
decidable: Dec(P)
Lemmas referenced :
deq_wf,
bag_wf,
all_wf,
deq-witness_wf,
sub-bag_wf,
equal_wf,
decidable_wf,
decidable__sub-bag,
bfalse_wf,
btrue_wf,
deq-exists,
decidable_functionality,
iff_preserves_decidability,
sub-bag-iff,
decidable__assert
Rules used in proof :
universeEquality,
because_Cache,
isect_memberEquality,
hypothesisEquality,
thin,
isectElimination,
extract_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
sqequalRule,
hypothesis,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
independent_functionElimination,
dependent_functionElimination,
lambdaFormation,
functionEquality,
cumulativity,
isectEquality,
lambdaEquality,
instantiate,
applyEquality,
unionElimination,
functionExtensionality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as,bs:bag(T)]. (deq-sub-bag(eq;as;bs) \mmember{} \mBbbB{})
Date html generated:
2020_05_20-AM-09_04_45
Last ObjectModification:
2020_01_28-PM-04_15_57
Theory : bags_2
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