Nuprl Lemma : cube-_wf
∀[I:fset(ℕ)]. ∀[i:ℕ]. (cube-(I;i) ∈ formal-cube(I+i) j⟶ formal-cube(I).𝕀)
Proof
Definitions occuring in Statement :
cube-: cube-(I;i)
,
interval-type: 𝕀
,
cube-context-adjoin: X.A
,
cube_set_map: A ⟶ B
,
formal-cube: formal-cube(I)
,
add-name: I+i
,
fset: fset(T)
,
nat: ℕ
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
Definitions unfolded in proof :
nat-trans: nat-trans(C;D;F;G)
,
psc_map: A ⟶ B
,
cube_set_map: A ⟶ B
,
member: t ∈ T
,
uall: ∀[x:A]. B[x]
,
prop: ℙ
,
nat: ℕ
,
names: names(I)
,
istype: istype(T)
,
uimplies: b supposing a
,
so_apply: x[s]
,
so_lambda: λ2x.t[x]
,
subtype_rel: A ⊆r B
,
names-hom: I ⟶ J
,
interval-presheaf: 𝕀
,
cube-: cube-(I;i)
,
all: ∀x:A. B[x]
,
cube-context-adjoin: X.A
,
pi1: fst(t)
,
pi2: snd(t)
,
spreadn: spread4,
cube-cat: CubeCat
,
cat-ob: cat-ob(C)
,
op-cat: op-cat(C)
,
cat-arrow: cat-arrow(C)
,
type-cat: TypeCat
,
functor-ob: ob(F)
,
formal-cube: formal-cube(I)
,
functor-arrow: arrow(F)
,
compose: f o g
,
guard: {T}
,
and: P ∧ Q
,
DeMorgan-algebra: DeMorganAlgebra
,
fset: fset(T)
,
cube-set-restriction: f(s)
,
I_cube: A(I)
Lemmas referenced :
nat_wf,
fset_wf,
istype-nat,
names-hom_wf,
strong-subtype-self,
istype-int,
le_wf,
strong-subtype-set3,
strong-subtype-deq-subtype,
int-deq_wf,
fset-member_wf,
trivial-member-add-name1,
f-subset-add-name,
names-subtype,
dM_wf,
lattice-point_wf,
add-name_wf,
names_wf,
subtype_rel_dep_function,
interval-type-at,
I_cube_pair_redex_lemma,
cube_set_restriction_pair_lemma,
arrow_pair_lemma,
cat_comp_tuple_lemma,
nh-comp_wf,
f-subset_weakening,
names-hom-subtype,
interval-type-ap-morph,
nh-comp-sq,
dM-lift_wf2,
DeMorgan-algebra-axioms_wf,
lattice-join_wf,
lattice-meet_wf,
equal_wf,
bounded-lattice-axioms_wf,
bounded-lattice-structure_wf,
subtype_rel_transitivity,
DeMorgan-algebra-structure-subtype,
bounded-lattice-structure-subtype,
lattice-axioms_wf,
lattice-structure_wf,
DeMorgan-algebra-structure_wf,
subtype_rel_set,
subtype_rel_self,
cube-set-restriction_wf,
interval-type_wf,
cube-context-adjoin_wf,
formal-cube_wf1,
I_cube_wf,
cat-arrow_wf,
cube-cat_wf,
op-cat_wf,
cat-ob_wf,
cat_arrow_triple_lemma
Rules used in proof :
thin,
isectElimination,
sqequalHypSubstitution,
universeIsType,
hypothesis,
extract_by_obid,
introduction,
cut,
dependent_set_memberEquality_alt,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
natural_numberEquality,
intEquality,
lambdaFormation_alt,
independent_isectElimination,
because_Cache,
lambdaEquality_alt,
applyEquality,
hypothesisEquality,
dependent_pairEquality_alt,
functionExtensionality,
Error :memTop,
dependent_functionElimination,
sqequalRule,
inhabitedIsType,
isectEquality,
cumulativity,
productEquality,
instantiate,
equalityIstype,
functionIsType
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[i:\mBbbN{}]. (cube-(I;i) \mmember{} formal-cube(I+i) j{}\mrightarrow{} formal-cube(I).\mBbbI{})
Date html generated:
2020_05_20-PM-02_38_43
Last ObjectModification:
2020_04_04-PM-01_34_57
Theory : cubical!type!theory
Home
Index