Nuprl Lemma : cu-cube-filler_wf
∀[I:Cname List]. ∀[alpha:c𝕌(I)].
(cu-cube-filler(alpha) ∈ L:(Cname List)
⟶ f:name-morph(I;L)
⟶ J:(nameset(L) List)
⟶ x:nameset(L)
⟶ i:ℕ2
⟶ A-open-box(unit-cube(I);Kan-type(alpha);L;f;J;x;i)
⟶ cu-cube-family(alpha;L;f))
Proof
Definitions occuring in Statement :
cu-cube-filler: cu-cube-filler(alpha),
cu-cube-family: cu-cube-family(alpha;L;f),
cubical-universe: c𝕌,
Kan-type: Kan-type(Ak),
A-open-box: A-open-box(X;A;I;alpha;J;x;i),
unit-cube: unit-cube(I),
I-cube: X(I),
name-morph: name-morph(I;J),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cu-cube-filler: cu-cube-filler(alpha),
cu-cube-family: cu-cube-family(alpha;L;f),
Kan-type: Kan-type(Ak),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
cubical-universe-I-cube,
I-cube_wf,
cubical-universe_wf,
list_wf,
coordinate_name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[I:Cname List]. \mforall{}[alpha:c\mBbbU{}(I)].
(cu-cube-filler(alpha) \mmember{} L:(Cname List)
{}\mrightarrow{} f:name-morph(I;L)
{}\mrightarrow{} J:(nameset(L) List)
{}\mrightarrow{} x:nameset(L)
{}\mrightarrow{} i:\mBbbN{}2
{}\mrightarrow{} A-open-box(unit-cube(I);Kan-type(alpha);L;f;J;x;i)
{}\mrightarrow{} cu-cube-family(alpha;L;f))
Date html generated:
2016_06_16-PM-08_08_04
Last ObjectModification:
2015_12_28-PM-04_11_31
Theory : cubical!sets
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