Nuprl Lemma : callbyvalueall-single-bag-combine1
∀[F,a,as:Top]. (let x ⟵ [a] in let y ⟵ ⋃z∈x.map(z;as) in F[y] ~ let x ⟵ a in let y ⟵ map(x;as) in F[y])
Proof
Definitions occuring in Statement :
bag-combine: ⋃x∈bs.f[x],
map: map(f;as),
cons: [a / b],
nil: [],
callbyvalueall: callbyvalueall,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
member: t ∈ T,
top: Top,
so_apply: x[s],
empty-bag: {},
bag-append: as + bs,
callbyvalueall: callbyvalueall,
uimplies: b supposing a,
has-valueall: has-valueall(a),
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ
Lemmas referenced :
has-valueall_wf_base,
evalall-sqequal,
cbv_sqequal,
top_wf,
map-append-empty,
bag-combine-unit-left-top,
callbyvalueall-single
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
because_Cache,
isect_memberFormation,
introduction,
sqequalAxiom,
hypothesisEquality,
baseApply,
closedConclusion,
baseClosed,
independent_isectElimination,
lambdaFormation
Latex:
\mforall{}[F,a,as:Top].
(let x \mleftarrow{}{} [a]
in let y \mleftarrow{}{} \mcup{}z\mmember{}x.map(z;as)
in F[y] \msim{} let x \mleftarrow{}{} a
in let y \mleftarrow{}{} map(x;as)
in F[y])
Date html generated:
2016_05_15-PM-03_09_23
Last ObjectModification:
2016_01_16-AM-08_33_43
Theory : bags
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