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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