Nuprl Lemma : sub_ps_context_wf
∀[C:SmallCategory]. ∀[Y,X:ps_context{j:l}(C)]. (sub_ps_context{j:l}(C; Y; X) ∈ 𝕌{[i | j'']})
Proof
Definitions occuring in Statement :
sub_ps_context: Y ⊆ X,
ps_context: __⊢,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type,
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
sub_ps_context: Y ⊆ X,
pscm-id: 1(X),
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
equal-wf-base,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf,
psc_map_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
thin,
instantiate,
introduction,
extract_by_obid,
because_Cache,
universeIsType,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
baseClosed
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[Y,X:ps\_context\{j:l\}(C)]. (sub\_ps\_context\{j:l\}(C; Y; X) \mmember{} \mBbbU{}\{[i | j'']\})
Date html generated:
2020_05_20-PM-01_24_41
Last ObjectModification:
2020_04_01-AM-09_52_03
Theory : presheaf!models!of!type!theory
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