Nuprl Lemma : A-face-name_wf
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[I:Cname List]. ∀[alpha:X(I)]. ∀[f:A-face(X;A;I;alpha)].
(A-face-name(f) ∈ nameset(I) × ℕ2)
Proof
Definitions occuring in Statement :
A-face-name: A-face-name(f),
A-face: A-face(X;A;I;alpha),
cubical-type: {X ⊢ _},
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],
member: t ∈ T,
product: x:A × B[x],
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
A-face-name: A-face-name(f),
A-face: A-face(X;A;I;alpha),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
A-face_wf,
I-cube_wf,
list_wf,
coordinate_name_wf,
cubical-type_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
independent_pairEquality,
sqequalHypSubstitution,
productElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[I:Cname List]. \mforall{}[alpha:X(I)]. \mforall{}[f:A-face(X;A;I;alpha)].
(A-face-name(f) \mmember{} nameset(I) \mtimes{} \mBbbN{}2)
Date html generated:
2016_06_16-PM-05_49_37
Last ObjectModification:
2015_12_28-PM-04_30_49
Theory : cubical!sets
Home
Index