Nuprl Lemma : count-single
∀[P,x:Top].  (count(P;[x]) ~ if P x then 1 else 0 fi  + 0)
Proof
Definitions occuring in Statement : 
count: count(P;L)
, 
cons: [a / b]
, 
nil: []
, 
ifthenelse: if b then t else f fi 
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
apply: f a
, 
add: n + m
, 
natural_number: $n
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
count: count(P;L)
, 
all: ∀x:A. B[x]
, 
top: Top
Lemmas referenced : 
reduce_cons_lemma, 
reduce_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{}[P,x:Top].    (count(P;[x])  \msim{}  if  P  x  then  1  else  0  fi    +  0)
Date html generated:
2016_05_14-AM-07_41_33
Last ObjectModification:
2015_12_26-PM-02_51_20
Theory : list_1
Home
Index