Nuprl Lemma : cat-retraction_wf
∀[C:SmallCategory]. ∀[x,y:cat-ob(C)]. ∀[g:cat-arrow(C) y x]. (retraction(g) ∈ ℙ)
Proof
Definitions occuring in Statement :
cat-retraction: retraction(g),
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
apply: f a
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
cat-retraction: retraction(g),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
cat-arrow_wf,
cat-inverse_wf,
cat-ob_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[x,y:cat-ob(C)]. \mforall{}[g:cat-arrow(C) y x]. (retraction(g) \mmember{} \mBbbP{})
Date html generated:
2020_05_20-AM-07_49_55
Last ObjectModification:
2017_01_08-PM-00_35_19
Theory : small!categories
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