Nuprl Lemma : bag-count-empty
∀[eq,x:Top]. ((#x in {}) ~ 0)
Proof
Definitions occuring in Statement :
bag-count: (#x in bs),
empty-bag: {},
uall: ∀[x:A]. B[x],
top: Top,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag-count: (#x in bs),
count: count(P;L),
reduce: reduce(f;k;as),
list_ind: list_ind,
empty-bag: {},
nil: [],
it: ⋅
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
sqequalAxiom,
extract_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[eq,x:Top]. ((\#x in \{\}) \msim{} 0)
Date html generated:
2018_05_21-PM-09_45_54
Last ObjectModification:
2018_05_19-PM-04_19_23
Theory : bags_2
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