Nuprl Lemma : small-category-subtype
SmallCategory ⊆r SmallCategory'
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,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
equal_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
productElimination,
dependent_set_memberEquality,
dependent_pairEquality,
cumulativity,
hypothesisEquality,
functionExtensionality,
applyEquality,
hypothesis,
because_Cache,
sqequalRule,
independent_pairEquality,
productEquality,
functionEquality,
universeEquality,
instantiate,
introduction,
extract_by_obid,
isectElimination
Latex:
SmallCategory \msubseteq{}r SmallCategory'
Date html generated:
2020_05_20-AM-07_49_23
Last ObjectModification:
2017_07_28-AM-09_18_55
Theory : small!categories
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