Nuprl Lemma : uniform-filling-function_wf
∀[Gamma:j⊢]. ∀[A:{Gamma ⊢ _}]. ∀[comp:filling-function{j:l, i:l}(Gamma;A)].
  (uniform-filling-function{j:l, i:l}(Gamma;A;comp) ∈ ℙ{[i' | j'']})
Proof
Definitions occuring in Statement : 
uniform-filling-function: uniform-filling-function{j:l, i:l}(Gamma;A;fill)
, 
filling-function: filling-function{j:l, i:l}(Gamma;A)
, 
cubical-type: {X ⊢ _}
, 
cubical_set: CubicalSet
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uniform-filling-function: uniform-filling-function{j:l, i:l}(Gamma;A;fill)
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
csm+: tau+
, 
csm-comp: G o F
, 
squash: ↓T
, 
csm-ap-term: (t)s
, 
cc-fst: p
, 
interval-type: 𝕀
, 
csm-ap: (s)x
, 
cc-snd: q
, 
constant-cubical-type: (X)
, 
csm-ap-type: (AF)s
, 
csm-adjoin: (s;u)
, 
pi1: fst(t)
, 
compose: f o g
, 
true: True
, 
cube_set_map: A ⟶ B
, 
psc_map: A ⟶ B
, 
nat-trans: nat-trans(C;D;F;G)
, 
cat-ob: cat-ob(C)
, 
op-cat: op-cat(C)
, 
spreadn: spread4, 
cube-cat: CubeCat
, 
fset: fset(T)
, 
quotient: x,y:A//B[x; y]
, 
cat-arrow: cat-arrow(C)
, 
pi2: snd(t)
, 
type-cat: TypeCat
, 
names-hom: I ⟶ J
, 
cat-comp: cat-comp(C)
, 
filling-function: filling-function{j:l, i:l}(Gamma;A)
, 
constrained-cubical-term: {Gamma ⊢ _:A[phi |⟶ t]}
, 
cubical-type: {X ⊢ _}
, 
interval-0: 0(𝕀)
, 
csm-id-adjoin: [u]
, 
csm-id: 1(X)
, 
subset-iota: iota
, 
partial-term-0: u[0]
Lemmas referenced : 
cubical_set_wf, 
cube_set_map_wf, 
cube-context-adjoin_wf, 
interval-type_wf, 
face-type_wf, 
cubical-term-eqcd, 
thin-context-subset, 
csm-ap-term_wf, 
csm-face-type, 
cc-fst_wf_interval, 
csm-ap-type_wf, 
context-subset_wf, 
constrained-cubical-term_wf, 
cubical_set_cumulativity-i-j, 
csm-id-adjoin_wf-interval-0, 
cubical-type-cumulativity2, 
partial-term-0_wf, 
filling-function_wf, 
cubical-type_wf, 
context-subset-map, 
csm+_wf_interval, 
istype-cubical-term, 
equal_wf, 
subtype_rel_self, 
csm-comp_wf, 
csm-comp-type, 
cubical-term_wf, 
squash_wf, 
true_wf, 
csm-context-subset-subtype2, 
csm-id-adjoin_wf, 
interval-0_wf, 
context-subset-term-subtype, 
cc-fst_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
cut, 
sqequalRule, 
functionEquality, 
cumulativity, 
thin, 
instantiate, 
introduction, 
extract_by_obid, 
hypothesis, 
because_Cache, 
sqequalHypSubstitution, 
isectElimination, 
hypothesisEquality, 
applyEquality, 
lambdaEquality_alt, 
universeIsType, 
universeEquality, 
equalityTransitivity, 
equalitySymmetry, 
independent_isectElimination, 
Error :memTop, 
imageElimination, 
inhabitedIsType, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed, 
hyp_replacement, 
setElimination, 
rename, 
dependent_set_memberEquality_alt, 
productElimination, 
equalityIstype
Latex:
\mforall{}[Gamma:j\mvdash{}].  \mforall{}[A:\{Gamma  \mvdash{}  \_\}].  \mforall{}[comp:filling-function\{j:l,  i:l\}(Gamma;A)].
    (uniform-filling-function\{j:l,  i:l\}(Gamma;A;comp)  \mmember{}  \mBbbP{}\{[i'  |  j'']\})
Date html generated:
2020_05_20-PM-04_41_12
Last ObjectModification:
2020_04_19-PM-02_03_09
Theory : cubical!type!theory
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