Nuprl Lemma : psc-m3_wf
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[A:{X ⊢ _}]. ∀[B:{X.A ⊢ _}]. ∀[E:{X.A.B ⊢ _}].
(q3 ∈ {X.A.B.E ⊢ _:(((A)p)p)p})
Proof
Definitions occuring in Statement :
psc-m3: q3,
psc-fst: p,
psc-adjoin: X.A,
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,
psc-m3: q3,
subtype_rel: A ⊆r B
Lemmas referenced :
pscm-ap-term_wf,
psc-adjoin_wf,
ps_context_cumulativity2,
presheaf-type-cumulativity2,
pscm-ap-type_wf,
psc-fst_wf,
psc-m2_wf,
presheaf-type_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,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
because_Cache,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[A:\{X \mvdash{} \_\}]. \mforall{}[B:\{X.A \mvdash{} \_\}]. \mforall{}[E:\{X.A.B \mvdash{} \_\}].
(q3 \mmember{} \{X.A.B.E \mvdash{} \_:(((A)p)p)p\})
Date html generated:
2020_05_20-PM-01_27_43
Last ObjectModification:
2020_04_02-PM-01_42_08
Theory : presheaf!models!of!type!theory
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