Nuprl Lemma : callbyvalueall-single-bag-combine3
∀[F,G,a,b:Top].
(let x ⟵ [a]
in let z ⟵ b
in let y ⟵ ⋃v∈x.G[z;v]
in F[z;y] ~ let x ⟵ a
in let z ⟵ b
in let y ⟵ G[z;x] @ []
in F[z;y])
Proof
Definitions occuring in Statement :
bag-combine: ⋃x∈bs.f[x],
append: as @ bs,
cons: [a / b],
nil: [],
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s1;s2],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nil: [],
it: ⋅,
cons: [a / b],
so_apply: x[s1;s2],
bag-combine: ⋃x∈bs.f[x],
bag-union: bag-union(bbs),
concat: concat(ll),
bag-map: bag-map(f;bs),
so_lambda: λ2x.t[x],
so_apply: x[s],
callbyvalueall: callbyvalueall,
evalall: evalall(t),
all: ∀x:A. B[x]
Lemmas referenced :
lifting-callbyvalueall-pair,
map_cons_lemma,
evalall_nil_lemma,
reduce_cons_lemma,
map_nil_lemma,
reduce_nil_lemma,
istype-top
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
Error :memTop,
hypothesis,
callbyvalueReduce,
sqleReflexivity,
dependent_functionElimination,
axiomSqEquality,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies
Latex:
\mforall{}[F,G,a,b:Top].
(let x \mleftarrow{}{} [a]
in let z \mleftarrow{}{} b
in let y \mleftarrow{}{} \mcup{}v\mmember{}x.G[z;v]
in F[z;y] \msim{} let x \mleftarrow{}{} a
in let z \mleftarrow{}{} b
in let y \mleftarrow{}{} G[z;x] @ []
in F[z;y])
Date html generated:
2020_05_20-AM-08_03_45
Last ObjectModification:
2020_01_17-AM-07_51_41
Theory : bags
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