Nuprl Lemma : bag-bind_wf
∀[A,B:Type]. ∀[bs:bag(A)]. ∀[f:A ⟶ bag(B)]. (bag-bind(bs;f) ∈ bag(B))
Proof
Definitions occuring in Statement :
bag-bind: bag-bind(bs;f),
bag: bag(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-bind: bag-bind(bs;f)
Lemmas referenced :
bag-union_wf,
bag-map_wf,
bag_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[bs:bag(A)]. \mforall{}[f:A {}\mrightarrow{} bag(B)]. (bag-bind(bs;f) \mmember{} bag(B))
Date html generated:
2016_05_15-PM-03_12_45
Last ObjectModification:
2015_12_27-AM-09_23_17
Theory : bags
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