Nuprl Lemma : small_ps_context_subtype
∀[C:SmallCategory]. (small_ps_context{j:l}(C) ⊆r ps_context{j:l}(C))
Proof
Definitions occuring in Statement :
small_ps_context: small_ps_context{i:l}(C),
ps_context: __⊢,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
small-category: SmallCategory
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
small_ps_context: small_ps_context{i:l}(C),
cat-functor: Functor(C1;C2),
ps_context: __⊢,
type-cat: TypeCat,
all: ∀x:A. B[x],
and: P ∧ Q
Lemmas referenced :
cat_arrow_triple_lemma,
cat_id_tuple_lemma,
cat_comp_tuple_lemma,
cat_ob_pair_lemma,
cat-ob_wf,
op-cat_wf,
cat-arrow_wf,
type-cat_wf,
cat-id_wf,
cat-comp_wf,
small_ps_context_wf,
small-category-cumulativity-2,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
lambdaEquality_alt,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality_alt,
sqequalRule,
extract_by_obid,
dependent_functionElimination,
Error :memTop,
hypothesis,
productElimination,
dependent_pairEquality_alt,
functionExtensionality,
cumulativity,
applyEquality,
hypothesisEquality,
isectElimination,
universeIsType,
functionEquality,
because_Cache,
universeEquality,
productIsType,
functionIsType,
equalityIstype,
instantiate,
axiomEquality
Latex:
\mforall{}[C:SmallCategory]. (small\_ps\_context\{j:l\}(C) \msubseteq{}r ps\_context\{j:l\}(C))
Date html generated:
2020_05_20-PM-01_23_02
Last ObjectModification:
2020_04_01-AM-10_42_41
Theory : presheaf!models!of!type!theory
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