Nuprl Lemma : for_nil_lemma
∀g,k,f,T:Top.  (For{T,f,k} x ∈ []. g[x] ~ k)
Proof
Definitions occuring in Statement : 
for: For{T,op,id} x ∈ as. f[x]
, 
nil: []
, 
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
, 
for: For{T,op,id} x ∈ as. f[x]
, 
top: Top
Lemmas referenced : 
top_wf, 
map_nil_lemma, 
reduce_nil_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{}g,k,f,T:Top.    (For\{T,f,k\}  x  \mmember{}  [].  g[x]  \msim{}  k)
Date html generated:
2016_05_14-AM-07_38_19
Last ObjectModification:
2015_12_26-PM-02_12_26
Theory : list_1
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