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
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