Nuprl Lemma : psc-snd-pscm-adjoin
∀[C:SmallCategory]. ∀[Gamma,Delta:ps_context{j:l}(C)]. ∀[A:{Gamma ⊢ _}]. ∀[sigma:psc_map{j:l}(C; Delta; Gamma)].
∀[u:{Delta ⊢ _:(A)sigma}].
((q)(sigma;u) = u ∈ {Delta ⊢ _:(A)sigma})
Proof
Definitions occuring in Statement :
pscm-adjoin: (s;u),
psc-snd: q,
pscm-ap-term: (t)s,
presheaf-term: {X ⊢ _:A},
pscm-ap-type: (AF)s,
presheaf-type: {X ⊢ _},
psc_map: A ⟶ B,
ps_context: __⊢,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
psc-snd-pscm-adjoin-sq,
pscm-ap-id-term,
pscm-ap-type_wf,
presheaf-term_wf,
psc_map_wf,
small-category-cumulativity-2,
presheaf-type_wf,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
Error :memTop,
sqequalRule,
hypothesis,
hypothesisEquality,
universeIsType,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
applyEquality,
because_Cache
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[Gamma,Delta:ps\_context\{j:l\}(C)]. \mforall{}[A:\{Gamma \mvdash{} \_\}]. \mforall{}[sigma:psc\_map\{j:l\}(C;
Delta;
Gamma
)].
\mforall{}[u:\{Delta \mvdash{} \_:(A)sigma\}].
((q)(sigma;u) = u)
Date html generated:
2020_05_20-PM-01_28_13
Last ObjectModification:
2020_04_02-PM-01_42_23
Theory : presheaf!models!of!type!theory
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