Nuprl Lemma : fills-open_box_wf
∀[X:CubicalSet]. ∀[I,J:Cname List]. ∀[x:nameset(I)]. ∀[i:ℕ2].
∀[bx:open_box(X;I;J;x;i)]. ∀[cube:X(I)]. (fills-open_box(X;I;bx;cube) ∈ ℙ) supposing l_subset(Cname;J;I)
Proof
Definitions occuring in Statement :
fills-open_box: fills-open_box(X;I;bx;cube),
open_box: open_box(X;I;J;x;i),
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-open_box: fills-open_box(X;I;bx;cube),
open_box: open_box(X;I;J;x;i),
prop: ℙ
Lemmas referenced :
fills-faces_wf,
I-cube_wf,
open_box_wf,
l_subset_wf,
coordinate_name_wf,
int_seg_wf,
nameset_wf,
list_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,
natural_numberEquality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[I,J:Cname List]. \mforall{}[x:nameset(I)]. \mforall{}[i:\mBbbN{}2].
\mforall{}[bx:open\_box(X;I;J;x;i)]. \mforall{}[cube:X(I)]. (fills-open\_box(X;I;bx;cube) \mmember{} \mBbbP{})
supposing l\_subset(Cname;J;I)
Date html generated:
2016_06_16-PM-06_42_57
Last ObjectModification:
2015_12_28-PM-04_26_16
Theory : cubical!sets
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