Nuprl Lemma : pscm-type-ap_wf
∀[C:SmallCategory]. ∀[Gamma,Delta:ps_context{j:l}(C)]. ∀[s:psc_map{j:l}(C; Delta; Gamma)]. ∀[A:{Gamma ⊢ _}].
(pscm-type-ap(A;s) ∈ Delta ⊢ )
Proof
Definitions occuring in Statement :
pscm-type-ap: pscm-type-ap(A;s),
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,
pscm-type-ap: pscm-type-ap(A;s),
subtype_rel: A ⊆r B
Lemmas referenced :
pscm-ap-type_wf,
presheaf-type_wf,
psc_map_wf,
small-category-cumulativity-2,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
applyEquality,
because_Cache
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[Gamma,Delta:ps\_context\{j:l\}(C)]. \mforall{}[s:psc\_map\{j:l\}(C; Delta; Gamma)].
\mforall{}[A:\{Gamma \mvdash{} \_\}].
(pscm-type-ap(A;s) \mmember{} Delta \mvdash{} )
Date html generated:
2020_05_20-PM-01_26_14
Last ObjectModification:
2020_04_01-AM-11_50_54
Theory : presheaf!models!of!type!theory
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