Nuprl Lemma : cu-cube-filler-uniform
∀[I:Cname List]. ∀[alpha:c𝕌(I)]. ∀[L:Cname List]. ∀[f:name-morph(I;L)]. ∀[J:nameset(L) List]. ∀[x:nameset(L)]. ∀[i:ℕ2].
∀[box:A-open-box(unit-cube(I);Kan-type(alpha);L;f;J;x;i)].
uniform-Kan-A-filler(unit-cube(I);Kan-type(alpha);cu-cube-filler(alpha))
Proof
Definitions occuring in Statement :
cu-cube-filler: cu-cube-filler(alpha),
cubical-universe: c𝕌,
Kan-type: Kan-type(Ak),
uniform-Kan-A-filler: uniform-Kan-A-filler(X;A;filler),
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],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
I-cube: X(I),
functor-ob: functor-ob(F),
pi1: fst(t),
cubical-universe: c𝕌,
Kan-cubical-type: {X ⊢ _(Kan)},
top: Top,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
name-morph: name-morph(I;J),
unit-cube: unit-cube(I),
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
uimplies: b supposing a,
nameset: nameset(L),
uniform-Kan-A-filler: uniform-Kan-A-filler(X;A;filler),
sq_stable: SqStable(P),
cu-cube-filler: cu-cube-filler(alpha),
Kan-type: Kan-type(Ak),
pi2: snd(t),
and: P ∧ Q,
squash: ↓T
Lemmas referenced :
cubical-universe-I-cube,
cubical-universe_wf,
l_member_wf,
I-cube_wf,
cu-cube-family_wf,
coordinate_name_wf,
subtype_rel_list,
equal_wf,
isname_wf,
assert_wf,
all_wf,
extd-nameset_wf,
A-open-box_wf,
int_seg_wf,
nameset_wf,
list_wf,
name-morph_wf,
subtype_rel_dep_function,
cu-cube-filler_wf,
cu-cube-family-Kan-type-at,
Kan-cubical-type_wf,
subtype_rel_self,
Kan-type_wf,
unit-cube_wf,
sq_stable_uniform-Kan-A-filler
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
sqequalRule,
instantiate,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
lambdaEquality,
functionEquality,
natural_numberEquality,
dependent_functionElimination,
setEquality,
independent_isectElimination,
setElimination,
rename,
lambdaFormation,
axiomEquality,
productElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}[I:Cname List]. \mforall{}[alpha:c\mBbbU{}(I)]. \mforall{}[L:Cname List]. \mforall{}[f:name-morph(I;L)]. \mforall{}[J:nameset(L) List].
\mforall{}[x:nameset(L)]. \mforall{}[i:\mBbbN{}2]. \mforall{}[box:A-open-box(unit-cube(I);Kan-type(alpha);L;f;J;x;i)].
uniform-Kan-A-filler(unit-cube(I);Kan-type(alpha);cu-cube-filler(alpha))
Date html generated:
2016_06_16-PM-08_08_16
Last ObjectModification:
2016_01_18-PM-04_44_47
Theory : cubical!sets
Home
Index