Nuprl Lemma : pscm-ap-type-fst-id-adjoin
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[B:{X ⊢ _}]. ∀[u:Top]. (((B)p)[u] = B ∈ {X ⊢ _})
Proof
Definitions occuring in Statement :
pscm-id-adjoin: [u],
psc-fst: p,
pscm-ap-type: (AF)s,
presheaf-type: {X ⊢ _},
ps_context: __⊢,
uall: ∀[x:A]. B[x],
top: Top,
equal: s = t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
pscm-id-adjoin: [u],
member: t ∈ T,
subtype_rel: A ⊆r B
Lemmas referenced :
pscm-ap-type-fst-adjoin,
small-category-cumulativity-2,
ps_context_cumulativity2,
presheaf-type-cumulativity2,
pscm-ap-id-type,
istype-top,
presheaf-type_wf,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
because_Cache,
Error :memTop,
universeIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[B:\{X \mvdash{} \_\}]. \mforall{}[u:Top]. (((B)p)[u] = B)
Date html generated:
2020_05_20-PM-01_28_22
Last ObjectModification:
2020_04_02-PM-01_56_01
Theory : presheaf!models!of!type!theory
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