Nuprl Lemma : bag-null-append
∀[T:Type]. ∀[as,bs:bag(T)]. bag-null(as + bs) = bag-null(as) ∧b bag-null(bs)
Proof
Definitions occuring in Statement :
bag-null: bag-null(bs),
bag-append: as + bs,
bag: bag(T),
band: p ∧b q,
bool: 𝔹,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
squash: ↓T,
exists: ∃x:A. B[x],
bag-null: bag-null(bs),
bag-append: as + bs,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
band: p ∧b q,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
and: P ∧ Q,
bfalse: ff,
prop: ℙ
Lemmas referenced :
bag_to_squash_list,
null_append,
subtype_rel_list,
top_wf,
null_wf,
bool_wf,
eqtt_to_assert,
assert_of_null,
equal_wf,
bag-null_wf,
bag-append_wf,
list-subtype-bag,
band_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
imageElimination,
productElimination,
promote_hyp,
hypothesis,
rename,
sqequalRule,
applyEquality,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
cumulativity,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
hyp_replacement,
applyLambdaEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:bag(T)]. bag-null(as + bs) = bag-null(as) \mwedge{}\msubb{} bag-null(bs)
Date html generated:
2017_10_01-AM-08_45_34
Last ObjectModification:
2017_07_26-PM-04_30_49
Theory : bags
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