Nuprl Lemma : bag_to_squash_list
∀[T:Type]. ∀[b:bag(T)]. (↓∃L:T List. (b = L ∈ bag(T)))
Proof
Definitions occuring in Statement :
bag: bag(T),
list: T List,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag: bag(T),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ,
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
squash: ↓T
Lemmas referenced :
squash_wf,
exists_wf,
list_wf,
equal_wf,
bag_wf,
list-subtype-bag,
permutation_wf,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
extract_by_obid,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
applyEquality,
because_Cache,
independent_isectElimination,
pertypeElimination,
productElimination,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
rename,
dependent_pairFormation,
imageMemberEquality,
baseClosed,
dependent_functionElimination,
independent_functionElimination,
productEquality,
imageElimination,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[b:bag(T)]. (\mdownarrow{}\mexists{}L:T List. (b = L))
Date html generated:
2017_10_01-AM-08_44_54
Last ObjectModification:
2017_07_26-PM-04_30_25
Theory : bags
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