Nuprl Lemma : op-cat-arrow
∀C:SmallCategory. ∀[A,B:Top]. (cat-arrow(op-cat(C)) A B ~ cat-arrow(C) B A)
Proof
Definitions occuring in Statement :
op-cat: op-cat(C),
cat-arrow: cat-arrow(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
small-category: SmallCategory,
spreadn: spread4,
op-cat: op-cat(C),
top: Top
Lemmas referenced :
cat_arrow_triple_lemma,
top_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
extract_by_obid,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
axiomSqEquality,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}C:SmallCategory. \mforall{}[A,B:Top]. (cat-arrow(op-cat(C)) A B \msim{} cat-arrow(C) B A)
Date html generated:
2020_05_20-AM-07_52_12
Last ObjectModification:
2017_01_10-PM-06_44_36
Theory : small!categories
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