Nuprl Lemma : pscm-ap-comp-term
∀[C:SmallCategory]. ∀[Gamma,Delta,Z:ps_context{j:l}(C)]. ∀[s1:psc_map{j:l}(C; Z; Delta)]. ∀[s2:psc_map{j:l}(C;
                                                                                                            Delta;
                                                                                                            Gamma)].
∀[A:{Gamma ⊢ _}]. ∀[t:{Gamma ⊢ _:A}].
  ((t)s2 o s1 = ((t)s2)s1 ∈ {Z ⊢ _:(A)s2 o s1})
Proof
Definitions occuring in Statement : 
pscm-ap-term: (t)s
, 
presheaf-term: {X ⊢ _:A}
, 
pscm-ap-type: (AF)s
, 
presheaf-type: {X ⊢ _}
, 
pscm-comp: G o F
, 
psc_map: A ⟶ B
, 
ps_context: __⊢
, 
uall: ∀[x:A]. B[x]
, 
equal: s = t ∈ T
, 
small-category: SmallCategory
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
squash: ↓T
, 
true: True
Lemmas referenced : 
pscm-comp-term, 
pscm-ap-term_wf, 
pscm-ap-type_wf, 
subtype_rel-equal, 
presheaf-term_wf, 
pscm-comp_wf, 
small-category-cumulativity-2, 
pscm-ap-comp-type, 
presheaf-type-cumulativity2, 
psc_map_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
Error :memTop, 
hypothesis, 
hypothesisEquality, 
because_Cache, 
applyEquality, 
instantiate, 
independent_isectElimination, 
lambdaEquality_alt, 
imageElimination, 
equalitySymmetry, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed, 
universeIsType, 
isect_memberEquality_alt, 
axiomEquality, 
isectIsTypeImplies, 
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory].  \mforall{}[Gamma,Delta,Z:ps\_context\{j:l\}(C)].  \mforall{}[s1:psc\_map\{j:l\}(C;  Z;  Delta)].
\mforall{}[s2:psc\_map\{j:l\}(C;  Delta;  Gamma)].  \mforall{}[A:\{Gamma  \mvdash{}  \_\}].  \mforall{}[t:\{Gamma  \mvdash{}  \_:A\}].
    ((t)s2  o  s1  =  ((t)s2)s1)
Date html generated:
2020_05_20-PM-01_27_01
Last ObjectModification:
2020_04_01-PM-10_37_35
Theory : presheaf!models!of!type!theory
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