Nuprl Lemma : face-name_wf
∀[X:CubicalSet]. ∀[I:Cname List]. ∀[f:I-face(X;I)]. (face-name(f) ∈ nameset(I) × ℕ2)
Proof
Definitions occuring in Statement :
face-name: face-name(f),
I-face: I-face(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,
face-name: face-name(f),
I-face: I-face(X;I),
pi1: fst(t),
pi2: snd(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,
independent_pairEquality,
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)]. (face-name(f) \mmember{} nameset(I) \mtimes{} \mBbbN{}2)
Date html generated:
2016_06_16-PM-05_49_15
Last ObjectModification:
2015_12_28-PM-04_31_15
Theory : cubical!sets
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