Nuprl Lemma : psc_map_wf
∀[C:SmallCategory]. ∀[A,B:ps_context{j:l}(C)]. (psc_map{j:l}(C; A; B) ∈ 𝕌{[i | j'']})
Proof
Definitions occuring in Statement :
psc_map: A ⟶ B,
ps_context: __⊢,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
ps_context: __⊢,
psc_map: A ⟶ B,
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
nat-trans_wf,
op-cat_wf,
type-cat_wf,
small-category-cumulativity-2,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalHypSubstitution,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
applyEquality,
because_Cache,
hypothesis,
sqequalRule,
universeIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[A,B:ps\_context\{j:l\}(C)]. (psc\_map\{j:l\}(C; A; B) \mmember{} \mBbbU{}\{[i | j'']\})
Date html generated:
2020_05_20-PM-01_23_49
Last ObjectModification:
2020_03_31-PM-07_38_45
Theory : presheaf!models!of!type!theory
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