Nuprl Lemma : tupletype_cons_lemma
∀L,T:Top.  (tuple-type([T / L]) ~ if null(L) then T else T × tuple-type(L) fi )
Proof
Definitions occuring in Statement : 
tuple-type: tuple-type(L)
, 
null: null(as)
, 
cons: [a / b]
, 
ifthenelse: if b then t else f fi 
, 
top: Top
, 
all: ∀x:A. B[x]
, 
product: x:A × B[x]
, 
sqequal: s ~ t
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
tuple-type: tuple-type(L)
, 
so_lambda: so_lambda(x,y,z.t[x; y; z])
, 
top: Top
, 
so_apply: x[s1;s2;s3]
Lemmas referenced : 
top_wf, 
list_ind_cons_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{}L,T:Top.    (tuple-type([T  /  L])  \msim{}  if  null(L)  then  T  else  T  \mtimes{}  tuple-type(L)  fi  )
Date html generated:
2016_05_14-PM-03_57_26
Last ObjectModification:
2015_12_26-PM-07_22_14
Theory : tuples
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