Nuprl Lemma : bag-subtype-fset
∀[A:Type]. (bag(A) ⊆r fset(A))
Proof
Definitions occuring in Statement : 
bag: bag(T)
, 
fset: fset(T)
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
bag: bag(T)
, 
quotient: x,y:A//B[x; y]
, 
and: P ∧ Q
, 
fset: fset(T)
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
guard: {T}
, 
set-equal: set-equal(T;x;y)
Lemmas referenced : 
fset_wf, 
quotient-member-eq, 
list_wf, 
set-equal_wf, 
set-equal-equiv, 
equal-wf-base, 
permutation_wf, 
bag_wf, 
member-permutation
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lambdaEquality, 
sqequalHypSubstitution, 
pointwiseFunctionalityForEquality, 
extract_by_obid, 
isectElimination, 
thin, 
cumulativity, 
hypothesisEquality, 
hypothesis, 
sqequalRule, 
pertypeElimination, 
productElimination, 
independent_isectElimination, 
dependent_functionElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
productEquality, 
because_Cache, 
axiomEquality
Latex:
\mforall{}[A:Type].  (bag(A)  \msubseteq{}r  fset(A))
Date html generated:
2018_05_21-PM-06_24_04
Last ObjectModification:
2017_11_10-PM-04_45_12
Theory : bags
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