Nuprl Lemma : cat-comp-ident1
∀[C:SmallCategory]. ∀x,y:cat-ob(C). ∀f:cat-arrow(C) x y. ((cat-comp(C) x x y (cat-id(C) x) f) = f ∈ (cat-arrow(C) x y))
Proof
Definitions occuring in Statement :
cat-comp: cat-comp(C),
cat-id: cat-id(C),
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
and: P ∧ Q
Lemmas referenced :
cat-comp-ident,
cat-arrow_wf,
cat-ob_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
productElimination,
hypothesis,
applyEquality,
sqequalRule,
lambdaEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[C:SmallCategory]. \mforall{}x,y:cat-ob(C). \mforall{}f:cat-arrow(C) x y. ((cat-comp(C) x x y (cat-id(C) x) f) = f)
Date html generated:
2017_01_19-PM-02_52_00
Last ObjectModification:
2017_01_11-PM-02_09_10
Theory : small!categories
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