Nuprl Lemma : no-repeats-bag-partitions
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)].
bag-no-repeats(bag(T) × bag(T);bag-partitions(eq;bs)) supposing valueall-type(T)
Proof
Definitions occuring in Statement :
bag-partitions: bag-partitions(eq;bs),
bag-no-repeats: bag-no-repeats(T;bs),
bag: bag(T),
deq: EqDecider(T),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
bag-partitions: bag-partitions(eq;bs),
callbyvalueall: callbyvalueall,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
has-value: (a)↓,
has-valueall: has-valueall(a),
bag-no-repeats: bag-no-repeats(T;bs),
squash: ↓T,
product-deq: product-deq(A;B;a;b)
Lemmas referenced :
bag-deq_wf,
product-deq_wf,
no-repeats-bag-to-set,
valueall-type-has-valueall,
deq_wf,
valueall-type_wf,
product-valueall-type,
bag-valueall-type,
bag-splits_wf,
bag_wf,
evalall-reduce
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
callbyvalueReduce,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
independent_isectElimination,
because_Cache,
lambdaEquality,
independent_functionElimination,
lambdaFormation,
imageElimination,
imageMemberEquality,
baseClosed,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)].
bag-no-repeats(bag(T) \mtimes{} bag(T);bag-partitions(eq;bs)) supposing valueall-type(T)
Date html generated:
2016_05_15-PM-08_05_57
Last ObjectModification:
2016_01_16-PM-01_28_14
Theory : bags_2
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