Nuprl Lemma : name-morph-domain_wf
∀[I,J:Cname List]. ∀[f:name-morph(I;J)]. (name-morph-domain(f;I) ∈ Type)
Proof
Definitions occuring in Statement :
name-morph-domain: name-morph-domain(f;I),
name-morph: name-morph(I;J),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
name-morph-domain: name-morph-domain(f;I),
name-morph: name-morph(I;J),
nameset: nameset(L),
prop: ℙ
Lemmas referenced :
nameset_wf,
filter_wf5,
coordinate_name_wf,
isname_wf,
l_member_wf,
name-morph_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaEquality,
applyEquality,
setElimination,
rename,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[f:name-morph(I;J)]. (name-morph-domain(f;I) \mmember{} Type)
Date html generated:
2016_05_20-AM-09_30_23
Last ObjectModification:
2015_12_28-PM-04_47_02
Theory : cubical!sets
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