Nuprl Lemma : id_functor_wf
∀[A:SmallCategory]. (1 ∈ Functor(A;A))
Proof
Definitions occuring in Statement :
id_functor: 1,
cat-functor: Functor(C1;C2),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uimplies: b supposing a,
id_functor: 1,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
small-category_wf,
cat-id_wf,
cat-comp_wf,
cat-arrow_wf,
cat-ob_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
lambdaFormation,
independent_isectElimination,
applyEquality,
hypothesis,
lambdaEquality,
because_Cache,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:SmallCategory]. (1 \mmember{} Functor(A;A))
Date html generated:
2020_05_20-AM-07_53_35
Last ObjectModification:
2018_05_18-PM-04_41_59
Theory : small!categories
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