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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