Nuprl Lemma : cu-cube-restriction_wf
∀[I:Cname List]. ∀[alpha:c𝕌(I)]. ∀[L,J:Cname List]. ∀[f:name-morph(L;J)]. ∀[a:name-morph(I;L)].
∀[T:cu-cube-family(alpha;L;a)].
(cu-cube-restriction(alpha;L;J;f;a;T) ∈ cu-cube-family(alpha;J;(a o f)))
Proof
Definitions occuring in Statement :
cu-cube-restriction: cu-cube-restriction(alpha;L;J;f;a;T),
cu-cube-family: cu-cube-family(alpha;L;f),
cubical-universe: c𝕌,
I-cube: X(I),
name-comp: (f o g),
name-morph: name-morph(I;J),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cu-cube-restriction: cu-cube-restriction(alpha;L;J;f;a;T),
cu-cube-family: cu-cube-family(alpha;L;f),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
cubical-universe-I-cube,
cu-cube-family_wf,
name-morph_wf,
list_wf,
coordinate_name_wf,
I-cube_wf,
cubical-universe_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
productElimination,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
instantiate
Latex:
\mforall{}[I:Cname List]. \mforall{}[alpha:c\mBbbU{}(I)]. \mforall{}[L,J:Cname List]. \mforall{}[f:name-morph(L;J)]. \mforall{}[a:name-morph(I;L)].
\mforall{}[T:cu-cube-family(alpha;L;a)].
(cu-cube-restriction(alpha;L;J;f;a;T) \mmember{} cu-cube-family(alpha;J;(a o f)))
Date html generated:
2016_06_16-PM-08_07_34
Last ObjectModification:
2015_12_28-PM-04_11_51
Theory : cubical!sets
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