Nuprl Lemma : uext-ap-name
∀[I,J:Cname List]. ∀[g:name-morph(I;J)]. ∀[x:nameset(I)]. ((uext(g) x) = (g x) ∈ extd-nameset(J))
Proof
Definitions occuring in Statement :
name-morph: name-morph(I;J),
uext: uext(g),
extd-nameset: extd-nameset(L),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uext: uext(g),
nameset: nameset(L),
ifthenelse: if b then t else f fi ,
btrue: tt,
name-morph: name-morph(I;J)
Lemmas referenced :
isname-name,
nameset_wf,
name-morph_wf,
list_wf,
coordinate_name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
isect_memberEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[g:name-morph(I;J)]. \mforall{}[x:nameset(I)]. ((uext(g) x) = (g x))
Date html generated:
2016_05_20-AM-09_29_35
Last ObjectModification:
2015_12_28-PM-04_47_19
Theory : cubical!sets
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