Nuprl Lemma : typed-psc-fst_wf
∀[C:SmallCategory]. ∀[G:ps_context{j:l}(C)]. ∀[A:{G ⊢ _}].  (tp{i:l} ∈ psc_map{[i | j]:l}(C; G.A; G))
Proof
Definitions occuring in Statement : 
typed-psc-fst: tp{i:l}
, 
psc-adjoin: X.A
, 
presheaf-type: {X ⊢ _}
, 
psc_map: A ⟶ B
, 
ps_context: __⊢
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
small-category: SmallCategory
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
typed-psc-fst: tp{i:l}
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
psc-fst_wf, 
small-category-cumulativity-2, 
ps_context_cumulativity2, 
presheaf-type-cumulativity2, 
presheaf-type_wf, 
ps_context_wf, 
small-category_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
thin, 
instantiate, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
hypothesisEquality, 
applyEquality, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeIsType, 
isect_memberEquality_alt, 
isectIsTypeImplies, 
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory].  \mforall{}[G:ps\_context\{j:l\}(C)].  \mforall{}[A:\{G  \mvdash{}  \_\}].
    (tp\{i:l\}  \mmember{}  psc\_map\{[i  |  j]:l\}(C;  G.A;  G))
Date html generated:
2020_05_20-PM-01_27_33
Last ObjectModification:
2020_04_03-AM-11_57_39
Theory : presheaf!models!of!type!theory
Home
Index