Nuprl Lemma : bag_combine_empty_lemma
∀f:Top. (⋃x∈{}.f[x] ~ {})
Proof
Definitions occuring in Statement :
bag-combine: ⋃x∈bs.f[x],
empty-bag: {},
top: Top,
so_apply: x[s],
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
bag-combine: ⋃x∈bs.f[x],
top: Top
Lemmas referenced :
top_wf,
bag_map_empty_lemma,
bag_union_empty_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}f:Top. (\mcup{}x\mmember{}\{\}.f[x] \msim{} \{\})
Date html generated:
2016_05_15-PM-02_28_04
Last ObjectModification:
2015_12_27-AM-09_51_05
Theory : bags
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