Nuprl Lemma : bag-combine-empty-left
∀[f:Top]. (⋃x∈{}.f[x] ~ {})
Proof
Definitions occuring in Statement :
bag-combine: ⋃x∈bs.f[x],
empty-bag: {},
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s]
Lemmas referenced :
bag_combine_empty_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom
Latex:
\mforall{}[f:Top]. (\mcup{}x\mmember{}\{\}.f[x] \msim{} \{\})
Date html generated:
2016_05_15-PM-02_28_20
Last ObjectModification:
2015_12_27-AM-09_50_27
Theory : bags
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