Nuprl Lemma : bag_all-empty
∀[f:Top]. (bag_all({};f) ~ tt)
Proof
Definitions occuring in Statement :
bag_all: bag_all(b;f),
empty-bag: {},
btrue: tt,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
empty-bag: {},
bag_all: bag_all(b;f),
bag-accum: bag-accum(v,x.f[v; x];init;bs),
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uall: ∀[x:A]. B[x]
Lemmas referenced :
list_accum_nil_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[f:Top]. (bag\_all(\{\};f) \msim{} tt)
Date html generated:
2016_05_15-PM-02_34_37
Last ObjectModification:
2015_12_27-AM-09_46_40
Theory : bags
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