Nuprl Lemma : cubical_set_cumulativity-i-j
CubicalSet ⊆r cubical_set{[j | i]:l}
Proof
Definitions occuring in Statement : 
cubical_set: CubicalSet
, 
subtype_rel: A ⊆r B
Definitions unfolded in proof : 
subtype_rel: A ⊆r B
, 
member: t ∈ T
, 
cubical_set: CubicalSet
, 
ps_context: __⊢
, 
cat-functor: Functor(C1;C2)
, 
type-cat: TypeCat
, 
cat-ob: cat-ob(C)
, 
pi1: fst(t)
, 
uall: ∀[x:A]. B[x]
, 
cat-arrow: cat-arrow(C)
, 
pi2: snd(t)
, 
cat-comp: cat-comp(C)
, 
cat-id: cat-id(C)
, 
and: P ∧ Q
, 
all: ∀x:A. B[x]
Lemmas referenced : 
cat-ob_wf, 
op-cat_wf, 
cube-cat_wf, 
subtype_rel_self, 
cat-arrow_wf, 
type-cat_wf, 
cat-id_wf, 
cat-comp_wf, 
cubical_set_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaEquality_alt, 
sqequalHypSubstitution, 
setElimination, 
thin, 
rename, 
cut, 
dependent_set_memberEquality_alt, 
productElimination, 
dependent_pairEquality_alt, 
functionExtensionality, 
applyEquality, 
hypothesisEquality, 
sqequalRule, 
cumulativity, 
universeIsType, 
universeEquality, 
hypothesis, 
introduction, 
extract_by_obid, 
isectElimination, 
instantiate, 
functionEquality, 
because_Cache, 
functionIsType, 
productIsType, 
equalityIstype
Latex:
CubicalSet  \msubseteq{}r  cubical\_set\{[j  |  i]:l\}
Date html generated:
2020_05_20-PM-01_38_39
Last ObjectModification:
2020_04_03-PM-03_37_45
Theory : cubical!type!theory
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