Nuprl Lemma : single-valued-bag-single
∀[T:Type]. ∀[b:T].  single-valued-bag({b};T)
Proof
Definitions occuring in Statement : 
single-valued-bag: single-valued-bag(b;T)
, 
single-bag: {x}
, 
uall: ∀[x:A]. B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
uimplies: b supposing a
, 
top: Top
, 
le: A ≤ B
, 
and: P ∧ Q
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
single-valued-bag: single-valued-bag(b;T)
Lemmas referenced : 
single-valued-bag-if-le1, 
single-bag_wf, 
bag_size_single_lemma, 
false_wf, 
bag-member_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
because_Cache, 
dependent_functionElimination, 
hypothesisEquality, 
hypothesis, 
independent_isectElimination, 
sqequalRule, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
independent_pairFormation, 
lambdaFormation, 
natural_numberEquality, 
lambdaEquality, 
axiomEquality, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[b:T].    single-valued-bag(\{b\};T)
Date html generated:
2016_05_15-PM-02_42_36
Last ObjectModification:
2015_12_27-AM-09_39_43
Theory : bags
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