Nuprl Lemma : sq_stable_uniform-Kan-A-filler
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[filler:I:(Cname List)
⟶ alpha:X(I)
⟶ J:(nameset(I) List)
⟶ x:nameset(I)
⟶ i:ℕ2
⟶ A-open-box(X;A;I;alpha;J;x;i)
⟶ A(alpha)].
SqStable(uniform-Kan-A-filler(X;A;filler))
Proof
Definitions occuring in Statement :
uniform-Kan-A-filler: uniform-Kan-A-filler(X;A;filler),
A-open-box: A-open-box(X;A;I;alpha;J;x;i),
cubical-type-at: A(a),
cubical-type: {X ⊢ _},
I-cube: X(I),
cubical-set: CubicalSet,
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
int_seg: {i..j-},
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
uniform-Kan-A-filler: uniform-Kan-A-filler(X;A;filler),
all: ∀x:A. B[x],
name-morph: name-morph(I;J),
prop: ℙ,
so_lambda: λ2x.t[x],
nameset: nameset(L),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s]
Lemmas referenced :
assert_wf,
isname_wf,
all_wf,
nameset_wf,
l_member_wf,
subtype_rel_list,
coordinate_name_wf,
name-morph_wf,
A-open-box_wf,
int_seg_wf,
list_wf,
I-cube_wf,
squash_wf,
uniform-Kan-A-filler_wf,
cubical-type-at_wf,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
imageElimination,
lambdaEquality,
axiomEquality,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
lemma_by_obid,
isectElimination,
applyEquality,
setElimination,
rename,
sqequalRule,
functionEquality,
because_Cache,
independent_isectElimination,
natural_numberEquality,
isect_memberEquality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[filler:I:(Cname List)
{}\mrightarrow{} alpha:X(I)
{}\mrightarrow{} J:(nameset(I) List)
{}\mrightarrow{} x:nameset(I)
{}\mrightarrow{} i:\mBbbN{}2
{}\mrightarrow{} A-open-box(X;A;I;alpha;J;x;i)
{}\mrightarrow{} A(alpha)].
SqStable(uniform-Kan-A-filler(X;A;filler))
Date html generated:
2016_06_16-PM-06_43_52
Last ObjectModification:
2015_12_28-PM-04_25_51
Theory : cubical!sets
Home
Index