Nuprl Lemma : list-subtype-bag
∀[A,B:Type]. (A List) ⊆r bag(B) supposing A ⊆r B
Proof
Definitions occuring in Statement :
bag: bag(T),
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
all: ∀x:A. B[x],
bag: bag(T),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q
Lemmas referenced :
list_wf,
permutation_wf,
permutation-equiv,
subtype_rel_list,
permutation_weakening,
quotient-member-eq,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
independent_isectElimination,
sqequalRule,
dependent_functionElimination,
because_Cache,
isect_memberFormation,
introduction,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. (A List) \msubseteq{}r bag(B) supposing A \msubseteq{}r B
Date html generated:
2016_05_15-PM-02_21_29
Last ObjectModification:
2015_12_27-AM-09_55_29
Theory : bags
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