Nuprl Lemma : cube-set-map-subtype
∀[A,B:CubicalSet].  (A ⟶ B ⊆r (I:(Cname List) ⟶ A(I) ⟶ B(I)))
Proof
Definitions occuring in Statement : 
I-cube: X(I)
, 
cube-set-map: A ⟶ B
, 
cubical-set: CubicalSet
, 
coordinate_name: Cname
, 
list: T List
, 
subtype_rel: A ⊆r B
, 
uall: ∀[x:A]. B[x]
, 
function: x:A ⟶ B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
subtype_rel: A ⊆r B
, 
member: t ∈ T
, 
cube-set-map: A ⟶ B
, 
nat-trans: nat-trans(C;D;F;G)
, 
I-cube: X(I)
, 
type-cat: TypeCat
, 
cat-arrow: cat-arrow(C)
, 
name-cat: NameCat
, 
cat-ob: cat-ob(C)
, 
pi1: fst(t)
, 
pi2: snd(t)
Lemmas referenced : 
cube-set-map_wf, 
cubical-set_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
lambdaEquality, 
sqequalHypSubstitution, 
setElimination, 
thin, 
rename, 
cut, 
hypothesis, 
introduction, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
sqequalRule
Latex:
\mforall{}[A,B:CubicalSet].    (A  {}\mrightarrow{}  B  \msubseteq{}r  (I:(Cname  List)  {}\mrightarrow{}  A(I)  {}\mrightarrow{}  B(I)))
Date html generated:
2018_05_23-PM-06_28_35
Last ObjectModification:
2018_05_20-PM-04_08_36
Theory : cubical!sets
Home
Index