Nuprl Lemma : name-morph-ap
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. ∀[x:nameset(I)].  (f x ∈ extd-nameset(J))
Proof
Definitions occuring in Statement : 
name-morph: name-morph(I;J)
, 
extd-nameset: extd-nameset(L)
, 
nameset: nameset(L)
, 
coordinate_name: Cname
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
apply: f a
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
name-morph: name-morph(I;J)
Lemmas referenced : 
nameset_wf, 
name-morph_wf, 
list_wf, 
coordinate_name_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
applyEquality, 
sqequalHypSubstitution, 
setElimination, 
thin, 
rename, 
hypothesisEquality, 
hypothesis, 
sqequalRule, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
lemma_by_obid, 
isectElimination, 
isect_memberEquality, 
because_Cache
Latex:
\mforall{}[I,J:Cname  List].  \mforall{}[f:name-morph(I;J)].  \mforall{}[x:nameset(I)].    (f  x  \mmember{}  extd-nameset(J))
Date html generated:
2016_05_20-AM-09_29_33
Last ObjectModification:
2015_12_28-PM-04_47_34
Theory : cubical!sets
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