Nuprl Lemma : ps-context-map-1
∀[C:SmallCategory]. ∀[I:cat-ob(C)]. (<cat-id(C) I> = 1(Yoneda(I)) ∈ Yoneda(I) ⟶ Yoneda(I))
Proof
Definitions occuring in Statement :
pscm-id: 1(X),
ps-context-map: <rho>,
psc_map: A ⟶ B,
Yoneda: Yoneda(I),
uall: ∀[x:A]. B[x],
apply: f a,
equal: s = t ∈ T,
cat-id: cat-id(C),
cat-ob: cat-ob(C),
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
cat-arrow: cat-arrow(C),
pi1: fst(t),
pi2: snd(t),
I_set: A(I),
functor-ob: ob(F),
Yoneda: Yoneda(I),
uimplies: b supposing a,
pscm-id: 1(X),
ps-context-map: <rho>,
and: P ∧ Q
Lemmas referenced :
cat-ob_wf,
small-category_wf,
Yoneda_wf,
ps-context-map_wf,
cat-id_wf,
subtype_rel_self,
I_set_wf,
pscm-id_wf,
pscm-equal2,
I_set_pair_redex_lemma,
arrow_pair_lemma,
cat-comp-ident,
cat-arrow_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesis,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
dependent_functionElimination,
applyEquality,
lambdaFormation_alt,
because_Cache,
independent_isectElimination,
Error :memTop,
productElimination
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[I:cat-ob(C)]. (<cat-id(C) I> = 1(Yoneda(I)))
Date html generated:
2020_05_20-PM-01_24_19
Last ObjectModification:
2020_04_03-PM-01_02_50
Theory : presheaf!models!of!type!theory
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