Nuprl Lemma : is-A-face_wf
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[I:Cname List]. ∀[alpha:X(I)]. ∀[bx:A(alpha)]. ∀[f:A-face(X;A;I;alpha)].
  (is-A-face(X;A;I;alpha;bx;f) ∈ ℙ)
Proof
Definitions occuring in Statement : 
is-A-face: is-A-face(X;A;I;alpha;bx;f)
, 
A-face: A-face(X;A;I;alpha)
, 
cubical-type-at: A(a)
, 
cubical-type: {X ⊢ _}
, 
I-cube: X(I)
, 
cubical-set: CubicalSet
, 
coordinate_name: Cname
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
is-A-face: is-A-face(X;A;I;alpha;bx;f)
, 
A-face: A-face(X;A;I;alpha)
, 
spreadn: spread3, 
nameset: nameset(L)
Lemmas referenced : 
equal_wf, 
cubical-type-at_wf, 
list-diff_wf, 
coordinate_name_wf, 
cname_deq_wf, 
cons_wf, 
nil_wf, 
cube-set-restriction_wf, 
face-map_wf2, 
cubical-type-ap-morph_wf, 
A-face_wf, 
I-cube_wf, 
list_wf, 
cubical-type_wf, 
cubical-set_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
sqequalHypSubstitution, 
productElimination, 
thin, 
lemma_by_obid, 
isectElimination, 
hypothesisEquality, 
hypothesis, 
because_Cache, 
setElimination, 
rename, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality
Latex:
\mforall{}[X:CubicalSet].  \mforall{}[A:\{X  \mvdash{}  \_\}].  \mforall{}[I:Cname  List].  \mforall{}[alpha:X(I)].  \mforall{}[bx:A(alpha)].
\mforall{}[f:A-face(X;A;I;alpha)].
    (is-A-face(X;A;I;alpha;bx;f)  \mmember{}  \mBbbP{})
Date html generated:
2016_06_16-PM-05_50_50
Last ObjectModification:
2015_12_28-PM-04_30_05
Theory : cubical!sets
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