Nuprl Lemma : functor_cat_comp_lemma
∀t2,t1,H,G,F,B,A:Top. (cat-comp(FUN(A;B)) F G H t1 t2 ~ t1 o t2)
Proof
Definitions occuring in Statement :
functor-cat: FUN(C1;C2),
trans-comp: t1 o t2,
cat-comp: cat-comp(C),
top: Top,
all: ∀x:A. B[x],
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
functor-cat: FUN(C1;C2),
top: Top
Lemmas referenced :
top_wf,
cat_comp_tuple_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalRule,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}t2,t1,H,G,F,B,A:Top. (cat-comp(FUN(A;B)) F G H t1 t2 \msim{} t1 o t2)
Date html generated:
2017_01_19-PM-02_53_02
Last ObjectModification:
2017_01_12-AM-11_11_33
Theory : small!categories
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