Nuprl Lemma : unit-cube-is-yoneda
∀[I:Cname List]. (unit-cube(I) = rep-pre-sheaf(op-cat(NameCat);I) ∈ CubicalSet)
Proof
Definitions occuring in Statement :
unit-cube: unit-cube(I),
cubical-set: CubicalSet,
name-cat: NameCat,
coordinate_name: Cname,
rep-pre-sheaf: rep-pre-sheaf(C;X),
op-cat: op-cat(C),
list: T List,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cubical-set: CubicalSet,
squash: ↓T,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ,
name-cat: NameCat,
op-cat: op-cat(C),
rep-pre-sheaf: rep-pre-sheaf(C;X),
unit-cube: unit-cube(I),
spreadn: spread4,
cat-comp: cat-comp(C),
cat-arrow: cat-arrow(C),
pi2: snd(t),
pi1: fst(t),
all: ∀x:A. B[x]
Lemmas referenced :
id-morph_wf,
equal-wf-T-base,
compose_wf,
name-comp_wf,
equal_wf,
all_wf,
name-morph_wf,
coordinate_name_wf,
list_wf,
set_wf,
unit-cube_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
hypothesis,
sqequalRule,
imageMemberEquality,
baseClosed,
instantiate,
productEquality,
functionEquality,
cumulativity,
universeEquality,
productElimination,
because_Cache,
introduction,
imageElimination,
dependent_set_memberEquality,
dependent_pairEquality
Latex:
\mforall{}[I:Cname List]. (unit-cube(I) = rep-pre-sheaf(op-cat(NameCat);I))
Date html generated:
2016_06_16-PM-05_37_53
Last ObjectModification:
2016_01_18-PM-04_57_00
Theory : cubical!sets
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