Nuprl Lemma : pscm-ap-comp-type-sq2
∀[C:SmallCategory]. ∀[Gamma:ps_context{j:l}(C)]. ∀[A:{Gamma ⊢ _}]. ∀[s1,s2:Top].  (((A)s2)s1 ~ (A)s2 o s1)
Proof
Definitions occuring in Statement : 
pscm-ap-type: (AF)s
, 
presheaf-type: {X ⊢ _}
, 
pscm-comp: G o F
, 
ps_context: __⊢
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
sqequal: s ~ t
, 
small-category: SmallCategory
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
istype-top, 
presheaf-type_wf, 
ps_context_wf, 
small-category-cumulativity-2, 
small-category_wf, 
pscm-ap-comp-type-sq
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
axiomSqEquality, 
because_Cache, 
cut, 
extract_by_obid, 
hypothesis, 
universeIsType, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
instantiate, 
applyEquality, 
sqequalRule, 
Error :memTop
Latex:
\mforall{}[C:SmallCategory].  \mforall{}[Gamma:ps\_context\{j:l\}(C)].  \mforall{}[A:\{Gamma  \mvdash{}  \_\}].  \mforall{}[s1,s2:Top].
    (((A)s2)s1  \msim{}  (A)s2  o  s1)
Date html generated:
2020_05_20-PM-01_26_29
Last ObjectModification:
2020_04_01-AM-11_00_57
Theory : presheaf!models!of!type!theory
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