Nuprl Lemma : bag-product-single
∀[bs:Top List]. ∀[a:Top]. ({a} × bs ~ bag-map(λx.<a, x>;bs))
Proof
Definitions occuring in Statement :
bag-product: bs × cs,
bag-map: bag-map(f;bs),
single-bag: {x},
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
lambda: λx.A[x],
pair: <a, b>,
sqequal: s ~ t
Definitions unfolded in proof :
bag-map: bag-map(f;bs),
single-bag: {x},
bag-product: bs × cs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
member: t ∈ T,
top: Top,
so_apply: x[s1;s2;s3],
empty-bag: {},
bag-append: as + bs,
uall: ∀[x:A]. B[x]
Lemmas referenced :
list_ind_cons_lemma,
list_ind_nil_lemma,
append_back_nil,
top_wf,
map_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
isectElimination,
productEquality,
lambdaEquality,
independent_pairEquality,
hypothesisEquality,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[bs:Top List]. \mforall{}[a:Top]. (\{a\} \mtimes{} bs \msim{} bag-map(\mlambda{}x.<a, x>bs))
Date html generated:
2016_05_15-PM-02_22_52
Last ObjectModification:
2015_12_27-AM-09_54_34
Theory : bags
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