Nuprl Lemma : name-morph-degeneracy-map
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. (degeneracy-map(f) ∈ name-morph(filter(λx.isname(f x);I);J))
Proof
Definitions occuring in Statement :
degeneracy-map: degeneracy-map(f),
name-morph: name-morph(I;J),
isname: isname(z),
coordinate_name: Cname,
filter: filter(P;l),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
lambda: λx.A[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph: name-morph(I;J),
nameset: nameset(L),
prop: ℙ,
name-morph-domain: name-morph-domain(f;I),
uimplies: b supposing a
Lemmas referenced :
name-morph_wf,
list_wf,
coordinate_name_wf,
degeneracy-map_wf,
filter_wf5,
isname_wf,
l_member_wf,
name-morph_subtype_domain,
name-morph-domain-inject
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
because_Cache,
lambdaEquality,
applyEquality,
setElimination,
rename,
setEquality,
independent_isectElimination
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)].
(degeneracy-map(f) \mmember{} name-morph(filter(\mlambda{}x.isname(f x);I);J))
Date html generated:
2016_05_20-AM-09_31_24
Last ObjectModification:
2015_12_28-PM-04_46_00
Theory : cubical!sets
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