Nuprl Lemma : single-valued-bag-list
∀[T:Type]. ∀[L:T List]. single-valued-list(L;T) supposing single-valued-bag(L;T)
Proof
Definitions occuring in Statement :
single-valued-bag: single-valued-bag(b;T),
single-valued-list: single-valued-list(L;T),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
single-valued-bag: single-valued-bag(b;T),
single-valued-list: single-valued-list(L;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
list-member-bag-member,
l_member_wf,
single-valued-bag_wf,
list-subtype-bag,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
lemma_by_obid,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
axiomEquality,
applyEquality,
independent_isectElimination,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. single-valued-list(L;T) supposing single-valued-bag(L;T)
Date html generated:
2016_05_15-PM-02_42_58
Last ObjectModification:
2015_12_27-AM-09_39_15
Theory : bags
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