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 :
top: Top,
op-cat: op-cat(C),
spreadn: spread4,
small-category: SmallCategory,
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x]
Lemmas referenced :
small-category_wf,
top_wf,
cat_arrow_triple_lemma
Rules used in proof :
because_Cache,
hypothesisEquality,
isectElimination,
sqequalAxiom,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
extract_by_obid,
sqequalRule,
productElimination,
rename,
thin,
setElimination,
sqequalHypSubstitution,
cut,
introduction,
isect_memberFormation,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}C:SmallCategory. \mforall{}[A,B:Top]. (cat-arrow(op-cat(C)) A B \msim{} cat-arrow(C) B A)
Date html generated:
2017_01_11-AM-09_18_25
Last ObjectModification:
2017_01_10-PM-06_44_36
Theory : small!categories
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