Nuprl Lemma : cat-id_wf
∀[C:SmallCategory]. (cat-id(C) ∈ x:cat-ob(C) ⟶ (cat-arrow(C) x x))
Proof
Definitions occuring in Statement :
cat-id: cat-id(C),
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
spreadn: spread4,
pi2: snd(t),
pi1: fst(t),
small-category: SmallCategory,
cat-id: cat-id(C),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
small-category_wf
Rules used in proof :
lemma_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
productElimination,
rename,
thin,
setElimination,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[C:SmallCategory]. (cat-id(C) \mmember{} x:cat-ob(C) {}\mrightarrow{} (cat-arrow(C) x x))
Date html generated:
2020_05_20-AM-07_49_33
Last ObjectModification:
2015_12_28-PM-02_24_05
Theory : small!categories
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