Nuprl Lemma : member-bag-to-set
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. ∀[x:T]. uiff(x ↓∈ bs;x ↓∈ bag-to-set(eq;bs))
Proof
Definitions occuring in Statement :
bag-to-set: bag-to-set(eq;bs),
bag-member: x ↓∈ bs,
bag: bag(T),
deq: EqDecider(T),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
bag-to-set: bag-to-set(eq;bs)
Lemmas referenced :
member-bag-remove-repeats
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
hypothesis
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)]. \mforall{}[x:T]. uiff(x \mdownarrow{}\mmember{} bs;x \mdownarrow{}\mmember{} bag-to-set(eq;bs))
Date html generated:
2016_05_15-PM-08_03_06
Last ObjectModification:
2015_12_27-PM-04_15_29
Theory : bags_2
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