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
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