Nuprl Lemma : ps_context_cumulativity2
∀[C:SmallCategory]. (ps_context{j:l}(C) ⊆r ps_context{[i | j]:l}(C))
Proof
Definitions occuring in Statement :
ps_context: __⊢,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
ps_context: __⊢,
cat-functor: Functor(C1;C2),
small-category: SmallCategory,
spreadn: spread4,
and: P ∧ Q,
type-cat: TypeCat,
cat-arrow: cat-arrow(C),
op-cat: op-cat(C),
cat-ob: cat-ob(C),
pi2: snd(t),
pi1: fst(t),
cat-comp: cat-comp(C),
cat-id: cat-id(C),
all: ∀x:A. B[x]
Lemmas referenced :
cat-ob_wf,
op-cat_wf,
cat-arrow_wf,
type-cat_wf,
cat-id_wf,
cat-comp_wf,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaEquality_alt,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality_alt,
productElimination,
dependent_pairEquality_alt,
sqequalRule,
functionExtensionality,
cumulativity,
applyEquality,
hypothesisEquality,
hypothesis,
functionIsType,
universeIsType,
because_Cache,
productIsType,
extract_by_obid,
isectElimination,
equalityIstype,
instantiate,
axiomEquality
Latex:
\mforall{}[C:SmallCategory]. (ps\_context\{j:l\}(C) \msubseteq{}r ps\_context\{[i | j]:l\}(C))
Date html generated:
2020_05_20-PM-01_23_06
Last ObjectModification:
2020_04_02-AM-11_44_28
Theory : presheaf!models!of!type!theory
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