Nuprl Lemma : bag-combine-restrict_wf
∀[A,B:Type]. ∀[b:bag(A)]. ∀[f:{a:A| a ↓∈ b} ⟶ bag(B)]. (bag-combine-restrict(b;x.f[x]) ∈ bag(B))
Proof
Definitions occuring in Statement :
bag-combine-restrict: bag-combine-restrict(b;x.f[x]),
bag-member: x ↓∈ bs,
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-combine-restrict: bag-combine-restrict(b;x.f[x]),
bag-combine: ⋃x∈bs.f[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
bag-union_wf,
bag-map_wf,
bag_wf,
bag-member_wf,
bag-subtype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setEquality,
lambdaEquality,
applyEquality,
cumulativity,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
axiomEquality,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[b:bag(A)]. \mforall{}[f:\{a:A| a \mdownarrow{}\mmember{} b\} {}\mrightarrow{} bag(B)]. (bag-combine-restrict(b;x.f[x]) \mmember{} bag(B))
Date html generated:
2016_05_15-PM-02_49_00
Last ObjectModification:
2015_12_27-AM-09_35_19
Theory : bags
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