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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