Nuprl Lemma : I_set_wf
∀[C:SmallCategory]. ∀[A:ps_context{j:l}(C)]. ∀[I:cat-ob(C)]. (A(I) ∈ 𝕌{j'})
Proof
Definitions occuring in Statement :
I_set: A(I),
ps_context: __⊢,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
cat-ob: cat-ob(C),
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ps_context: __⊢,
cat-functor: Functor(C1;C2),
and: P ∧ Q,
I_set: A(I),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
cat-ob: cat-ob(C),
pi1: fst(t),
type-cat: TypeCat
Lemmas referenced :
ob_pair_lemma,
subtype_rel-equal,
cat-ob_wf,
op-cat_wf,
cat_ob_op_lemma,
subtype_rel_self,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
applyEquality,
hypothesisEquality,
isectElimination,
independent_isectElimination,
instantiate,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[A:ps\_context\{j:l\}(C)]. \mforall{}[I:cat-ob(C)]. (A(I) \mmember{} \mBbbU{}\{j'\})
Date html generated:
2020_05_20-PM-01_23_12
Last ObjectModification:
2020_03_31-PM-02_12_14
Theory : presheaf!models!of!type!theory
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