Nuprl Lemma : bag-union-is-single-if
∀[T:Type]. ∀[x:T]. ∀bbs:bag(bag(T)). bag-union(bbs) = {x} ∈ bag(T) supposing bbs = {{x}} ∈ bag(bag(T))
Proof
Definitions occuring in Statement :
bag-union: bag-union(bbs),
single-bag: {x},
bag: bag(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
bag-union-single,
single-bag_wf,
bag-subtype-list,
equal_wf,
bag_wf,
bag-union_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
hypothesis,
thin,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
cumulativity,
hypothesisEquality,
applyEquality,
because_Cache,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
isectElimination,
lambdaEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}bbs:bag(bag(T)). bag-union(bbs) = \{x\} supposing bbs = \{\{x\}\}
Date html generated:
2016_10_25-AM-10_23_22
Last ObjectModification:
2016_07_12-AM-06_39_59
Theory : bags
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