Nuprl Lemma : pscm-ap-type-is-id
∀[C:SmallCategory]. ∀[Gamma:ps_context{j:l}(C)]. ∀[A:{Gamma ⊢ _}]. ∀[s:psc_map{j:l}(C; Gamma; Gamma)].
(A)s = A ∈ {Gamma ⊢ _} supposing s = 1(Gamma) ∈ psc_map{j:l}(C; Gamma; Gamma)
Proof
Definitions occuring in Statement :
pscm-ap-type: (AF)s,
presheaf-type: {X ⊢ _},
pscm-id: 1(X),
psc_map: A ⟶ B,
ps_context: __⊢,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B
Lemmas referenced :
pscm-ap-id-type,
equal_wf,
presheaf-type_wf,
pscm-ap-type_wf,
pscm-id_wf,
psc_map_wf,
small-category-cumulativity-2,
ps_context_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
hypothesis,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
instantiate,
equalityIstype,
inhabitedIsType,
sqequalRule,
isect_memberEquality_alt,
axiomEquality,
isectIsTypeImplies,
universeIsType,
applyEquality,
because_Cache
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[Gamma:ps\_context\{j:l\}(C)]. \mforall{}[A:\{Gamma \mvdash{} \_\}].
\mforall{}[s:psc\_map\{j:l\}(C; Gamma; Gamma)].
(A)s = A supposing s = 1(Gamma)
Date html generated:
2020_05_20-PM-01_26_23
Last ObjectModification:
2020_04_01-AM-11_50_58
Theory : presheaf!models!of!type!theory
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