Nuprl Lemma : fills-A-faces_wf
∀[X:CubicalSet]. ∀[A:{X ⊢ _}]. ∀[I:Cname List]. ∀[alpha:X(I)]. ∀[bx:A(alpha)]. ∀[L:A-face(X;A;I;alpha) List].
(fills-A-faces(X;A;I;alpha;bx;L) ∈ ℙ)
Proof
Definitions occuring in Statement :
fills-A-faces: fills-A-faces(X;A;I;alpha;bx;L),
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,
fills-A-faces: fills-A-faces(X;A;I;alpha;bx;L),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
l_all_wf2,
A-face_wf,
is-A-face_wf,
l_member_wf,
list_wf,
cubical-type-at_wf,
I-cube_wf,
coordinate_name_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,
hypothesis,
lambdaEquality,
setElimination,
rename,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[I:Cname List]. \mforall{}[alpha:X(I)]. \mforall{}[bx:A(alpha)].
\mforall{}[L:A-face(X;A;I;alpha) List].
(fills-A-faces(X;A;I;alpha;bx;L) \mmember{} \mBbbP{})
Date html generated:
2016_06_16-PM-05_51_06
Last ObjectModification:
2015_12_28-PM-04_29_55
Theory : cubical!sets
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