Nuprl Lemma : presheaf-id-fun_wf
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. ∀[A:{X ⊢ _}]. (presheaf-id-fun(X) ∈ {X ⊢ _:(A ⟶ A)})
Proof
Definitions occuring in Statement :
presheaf-id-fun: presheaf-id-fun(X),
presheaf-fun: (A ⟶ B),
presheaf-term: {X ⊢ _:A},
presheaf-type: {X ⊢ _},
ps_context: __⊢,
uall: ∀[x:A]. B[x],
member: t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
presheaf-id-fun: presheaf-id-fun(X),
subtype_rel: A ⊆r B
Lemmas referenced :
presheaf-lam_wf,
small-category-cumulativity-2,
ps_context_cumulativity2,
presheaf-type-cumulativity2,
psc-snd_wf,
presheaf-type_wf,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. \mforall{}[A:\{X \mvdash{} \_\}]. (presheaf-id-fun(X) \mmember{} \{X \mvdash{} \_:(A {}\mrightarrow{} A)\})
Date html generated:
2020_05_20-PM-01_30_29
Last ObjectModification:
2020_04_02-PM-03_02_21
Theory : presheaf!models!of!type!theory
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