Nuprl Lemma : functor_cat_id_lemma
∀F,B,A:Top. (cat-id(FUN(A;B)) F ~ identity-trans(A;B;F))
Proof
Definitions occuring in Statement :
functor-cat: FUN(C1;C2),
identity-trans: identity-trans(C;D;F),
cat-id: cat-id(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_id_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{}F,B,A:Top. (cat-id(FUN(A;B)) F \msim{} identity-trans(A;B;F))
Date html generated:
2017_01_19-PM-02_52_59
Last ObjectModification:
2017_01_12-AM-11_08_37
Theory : small!categories
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