Nuprl Lemma : bag-filter-no-repeats2
∀[T:Type]. ∀[p:T ⟶ 𝔹]. ∀[bs:bag(T)]. bag-no-repeats({x:T| ↑p[x]} ;[x∈bs|p[x]]) supposing bag-no-repeats(T;bs)
Proof
Definitions occuring in Statement :
bag-no-repeats: bag-no-repeats(T;bs),
bag-filter: [x∈b|p[x]],
bag: bag(T),
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x.t[x],
bag-no-repeats: bag-no-repeats(T;bs),
squash: ↓T
Lemmas referenced :
bool_wf,
bag_wf,
bag-no-repeats_wf,
strong-subtype-set2,
bag-filter_wf,
assert_wf,
bag-no-repeats-subtype,
bag-filter-no-repeats
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
independent_isectElimination,
setEquality,
applyEquality,
sqequalRule,
lambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[p:T {}\mrightarrow{} \mBbbB{}]. \mforall{}[bs:bag(T)]. bag-no-repeats(\{x:T| \muparrow{}p[x]\} ;[x\mmember{}bs|p[x]]) supposing bag-no-re\000Cpeats(T;bs)
Date html generated:
2016_05_15-PM-02_46_50
Last ObjectModification:
2016_01_16-AM-08_43_43
Theory : bags
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