Nuprl Lemma : pscm-ap-term-p
∀[C:SmallCategory]. ∀[Gamma:ps_context{j:l}(C)]. ∀[A,T:{Gamma ⊢ _}]. ∀[t:{Gamma ⊢ _:A}]. ((t)p ∈ {Gamma.T ⊢ _:(A)p})
Proof
Definitions occuring in Statement :
psc-fst: p,
psc-adjoin: X.A,
pscm-ap-term: (t)s,
presheaf-term: {X ⊢ _:A},
pscm-ap-type: (AF)s,
presheaf-type: {X ⊢ _},
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,
subtype_rel: A ⊆r B
Lemmas referenced :
pscm-ap-term_wf,
psc-adjoin_wf,
small-category-cumulativity-2,
ps_context_cumulativity2,
presheaf-type-cumulativity2,
psc-fst_wf,
presheaf-term_wf,
presheaf-type_wf,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[Gamma:ps\_context\{j:l\}(C)]. \mforall{}[A,T:\{Gamma \mvdash{} \_\}]. \mforall{}[t:\{Gamma \mvdash{} \_:A\}].
((t)p \mmember{} \{Gamma.T \mvdash{} \_:(A)p\})
Date html generated:
2020_05_20-PM-01_27_48
Last ObjectModification:
2020_04_02-PM-01_55_35
Theory : presheaf!models!of!type!theory
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