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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