Nuprl Lemma : bag-accum-single
∀[init,f,x:Top]. (bag-accum(v,x.f[v;x];init;{x}) ~ f[init;x])
Proof
Definitions occuring in Statement :
bag-accum: bag-accum(v,x.f[v; x];init;bs),
single-bag: {x},
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,
single-bag: {x},
bag-accum: bag-accum(v,x.f[v; x];init;bs),
all: ∀x:A. B[x],
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
list_accum_cons_lemma,
list_accum_nil_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[init,f,x:Top]. (bag-accum(v,x.f[v;x];init;\{x\}) \msim{} f[init;x])
Date html generated:
2016_05_15-PM-02_30_07
Last ObjectModification:
2015_12_27-AM-09_49_04
Theory : bags
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