Nuprl Lemma : bag-combine-member-wf
∀[A,B:Type]. ∀[bs:bag(A)]. ∀[f:{a:A| a ↓∈ bs} ⟶ bag(B)]. (⋃x∈bs.f[x] ∈ bag(B))
Proof
Definitions occuring in Statement :
bag-member: x ↓∈ bs,
bag-combine: ⋃x∈bs.f[x],
bag: bag(T),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
bag-combine: ⋃x∈bs.f[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
bag-union_wf,
bag-map-member-wf,
bag_wf,
bag-member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
setEquality,
functionEquality,
because_Cache,
universeEquality,
isect_memberFormation,
introduction,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[bs:bag(A)]. \mforall{}[f:\{a:A| a \mdownarrow{}\mmember{} bs\} {}\mrightarrow{} bag(B)]. (\mcup{}x\mmember{}bs.f[x] \mmember{} bag(B))
Date html generated:
2016_05_15-PM-02_47_06
Last ObjectModification:
2015_12_27-AM-09_36_24
Theory : bags
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