Nuprl Lemma : cube-set-restriction-id
∀[X:CubicalSet]. ∀[I:Cname List]. ∀[s:X(I)]. (1(s) = s ∈ X(I))
Proof
Definitions occuring in Statement :
cube-set-restriction: f(s)
,
I-cube: X(I)
,
cubical-set: CubicalSet
,
id-morph: 1
,
coordinate_name: Cname
,
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
,
cube-set-restriction: f(s)
,
pi2: snd(t)
,
and: P ∧ Q
,
squash: ↓T
,
prop: ℙ
,
all: ∀x:A. B[x]
,
I-cube: X(I)
,
top: Top
,
subtype_rel: A ⊆r B
,
functor-ob: ob(F)
,
pi1: fst(t)
,
true: True
,
uimplies: b supposing a
,
guard: {T}
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
,
implies: P
⇒ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
I-cube_wf,
ob_pair_lemma,
subtype_rel_self,
list_wf,
coordinate_name_wf,
iff_weakening_equal,
cubical-set_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
applyEquality,
lambdaEquality,
imageElimination,
extract_by_obid,
isectElimination,
equalityTransitivity,
hypothesis,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
functionExtensionality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination,
axiomEquality,
because_Cache
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[I:Cname List]. \mforall{}[s:X(I)]. (1(s) = s)
Date html generated:
2017_10_05-AM-10_11_51
Last ObjectModification:
2017_07_28-AM-11_17_57
Theory : cubical!sets
Home
Index