Nuprl Lemma : small-category-cumulativity-2
SmallCategory ⊆r small-category{[j | i]:l}
Proof
Definitions occuring in Statement :
small-category: SmallCategory,
subtype_rel: A ⊆r B
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
member: t ∈ T,
small-category: SmallCategory,
spreadn: spread4,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
and: P ∧ Q
Lemmas referenced :
subtype_rel_dep_function,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality_alt,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
productElimination,
dependent_set_memberEquality_alt,
dependent_pairEquality_alt,
cumulativity,
hypothesisEquality,
functionExtensionality,
applyEquality,
hypothesis,
instantiate,
introduction,
extract_by_obid,
isectElimination,
sqequalRule,
universeEquality,
inhabitedIsType,
because_Cache,
independent_isectElimination,
universeIsType,
lambdaFormation_alt,
productEquality,
functionEquality,
productIsType,
functionIsType,
equalityIstype
Latex:
SmallCategory \msubseteq{}r small-category\{[j | i]:l\}
Date html generated:
2020_05_20-AM-07_49_26
Last ObjectModification:
2020_04_01-AM-00_46_17
Theory : small!categories
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