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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