Nuprl Lemma : fills-A-open-box_wf
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[I:Cname List]. ∀[alpha:X(I)]. ∀[J:Cname List]. ∀[x:nameset(I)]. ∀[i:ℕ2].
∀[cube:A(alpha)]. ∀[bx:A-open-box(X;A;I;alpha;J;x;i)].
fills-A-open-box(X;A;I;alpha;bx;cube) ∈ ℙ supposing l_subset(Cname;J;I)
Proof
Definitions occuring in Statement :
fills-A-open-box: fills-A-open-box(X;A;I;alpha;bx;cube),
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,
l_subset: l_subset(T;as;bs),
list: T List,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
fills-A-open-box: fills-A-open-box(X;A;I;alpha;bx;cube),
A-open-box: A-open-box(X;A;I;alpha;J;x;i),
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
fills-A-faces_wf,
l_subset_wf,
coordinate_name_wf,
A-open-box_wf,
cubical-type-at_wf,
int_seg_wf,
nameset_wf,
list_wf,
I-cube_wf,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
dependent_functionElimination,
natural_numberEquality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[I:Cname List]. \mforall{}[alpha:X(I)]. \mforall{}[J:Cname List]. \mforall{}[x:nameset(I)].
\mforall{}[i:\mBbbN{}2]. \mforall{}[cube:A(alpha)]. \mforall{}[bx:A-open-box(X;A;I;alpha;J;x;i)].
fills-A-open-box(X;A;I;alpha;bx;cube) \mmember{} \mBbbP{} supposing l\_subset(Cname;J;I)
Date html generated:
2016_06_16-PM-06_43_05
Last ObjectModification:
2015_12_28-PM-04_26_11
Theory : cubical!sets
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