Nuprl Lemma : sub_ps_context_self
∀[C:SmallCategory]. ∀[X:ps_context{j:l}(C)]. sub_ps_context{j:l}(C; X; X)
Proof
Definitions occuring in Statement :
sub_ps_context: Y ⊆ X,
ps_context: __⊢,
uall: ∀[x:A]. B[x],
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sub_ps_context: Y ⊆ X,
subtype_rel: A ⊆r B
Lemmas referenced :
sub_ps_context_weakening,
ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
instantiate,
applyEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[X:ps\_context\{j:l\}(C)]. sub\_ps\_context\{j:l\}(C; X; X)
Date html generated:
2020_05_20-PM-01_24_48
Last ObjectModification:
2020_04_01-AM-11_00_43
Theory : presheaf!models!of!type!theory
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