Nuprl Lemma : face-cube_wf
∀[X:CubicalSet]. ∀[I:Cname List]. ∀[f:I-face(X;I)]. (cube(f) ∈ X(I-[dimension(f)]))
Proof
Definitions occuring in Statement :
face-cube: cube(f),
face-dimension: dimension(f),
I-face: I-face(X;I),
I-cube: X(I),
cubical-set: CubicalSet,
cname_deq: CnameDeq,
coordinate_name: Cname,
list-diff: as-bs,
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
face-cube: cube(f),
I-face: I-face(X;I),
pi2: snd(t),
face-dimension: dimension(f),
pi1: fst(t)
Lemmas referenced :
I-face_wf,
list_wf,
coordinate_name_wf,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[I:Cname List]. \mforall{}[f:I-face(X;I)]. (cube(f) \mmember{} X(I-[dimension(f)]))
Date html generated:
2016_06_16-PM-05_48_57
Last ObjectModification:
2015_12_28-PM-04_31_27
Theory : cubical!sets
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