Nuprl Lemma : unit-cube-map-id
∀I:Cname List. (unit-cube-map(1) = 1(unit-cube(I)) ∈ unit-cube(I) ⟶ unit-cube(I))
Proof
Definitions occuring in Statement :
unit-cube-map: unit-cube-map(f),
unit-cube: unit-cube(I),
csm-id: 1(X),
cube-set-map: A ⟶ B,
id-morph: 1,
coordinate_name: Cname,
list: T List,
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
cube-set-map: A ⟶ B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
guard: {T},
uimplies: b supposing a,
nat-trans: nat-trans(C;D;F;G),
name-cat: NameCat,
cat-ob: cat-ob(C),
pi1: fst(t),
unit-cube-map: unit-cube-map(f),
unit-cube: unit-cube(I),
csm-id: 1(X),
top: Top,
type-cat: TypeCat,
cat-id: cat-id(C),
cat-arrow: cat-arrow(C),
pi2: snd(t),
squash: ↓T,
prop: ℙ,
true: True,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
cubical-set-is-functor,
list_wf,
coordinate_name_wf,
name-cat_wf,
type-cat_wf,
unit-cube_wf,
subtype_rel_weakening,
cubical-set_wf,
cat-functor_wf,
csm-id_wf,
unit-cube-map_wf,
id-morph_wf,
cube-set-map_wf,
nat-trans-equal,
cat-ob_wf,
ob_pair_lemma,
ident_trans_ap_lemma,
equal_wf,
squash_wf,
true_wf,
name-morph_wf,
name-comp-id-left,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
equalitySymmetry,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
instantiate,
hypothesisEquality,
applyEquality,
independent_isectElimination,
sqequalRule,
lambdaEquality,
setElimination,
rename,
functionExtensionality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
equalityTransitivity,
universeEquality,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}I:Cname List. (unit-cube-map(1) = 1(unit-cube(I)))
Date html generated:
2017_10_05-AM-10_12_13
Last ObjectModification:
2017_07_28-AM-11_18_09
Theory : cubical!sets
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