Nuprl Lemma : Kan-filler_wf
∀[X:CubicalSet]. ∀[filler:I:(Cname List) ⟶ J:(nameset(I) List) ⟶ x:nameset(I) ⟶ i:ℕ2 ⟶ open_box(X;I;J;x;i) ⟶ X(I)].
(Kan-filler(X;filler) ∈ ℙ)
Proof
Definitions occuring in Statement :
Kan-filler: Kan-filler(X;filler),
open_box: open_box(X;I;J;x;i),
I-cube: X(I),
cubical-set: CubicalSet,
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
Kan-filler: Kan-filler(X;filler),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nameset: nameset(L),
open_box: open_box(X;I;J;x;i),
so_apply: x[s],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T
Lemmas referenced :
decidable__equal-coordinate_name,
sq_stable__l_subset,
cubical-set_wf,
I-cube_wf,
fills-open_box_wf,
subtype_rel_list,
open_box_wf,
int_seg_wf,
nameset_wf,
coordinate_name_wf,
list_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
hypothesisEquality,
because_Cache,
natural_numberEquality,
applyEquality,
independent_isectElimination,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
productElimination,
dependent_functionElimination,
independent_functionElimination,
lambdaFormation,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[filler:I:(Cname List)
{}\mrightarrow{} J:(nameset(I) List)
{}\mrightarrow{} x:nameset(I)
{}\mrightarrow{} i:\mBbbN{}2
{}\mrightarrow{} open\_box(X;I;J;x;i)
{}\mrightarrow{} X(I)].
(Kan-filler(X;filler) \mmember{} \mBbbP{})
Date html generated:
2016_06_16-PM-06_49_17
Last ObjectModification:
2016_01_18-PM-04_51_49
Theory : cubical!sets
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