Nuprl Lemma : cat-arrow_wf
∀[C:SmallCategory]. (cat-arrow(C) ∈ x:cat-ob(C) ⟶ y:cat-ob(C) ⟶ Type)
Proof
Definitions occuring in Statement :
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
small-category: SmallCategory,
spreadn: spread4,
and: P ∧ Q,
cat-arrow: cat-arrow(C),
all: ∀x:A. B[x],
top: Top,
pi2: snd(t),
pi1: fst(t)
Lemmas referenced :
cat_ob_pair_lemma,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
introduction,
extract_by_obid,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality
Latex:
\mforall{}[C:SmallCategory]. (cat-arrow(C) \mmember{} x:cat-ob(C) {}\mrightarrow{} y:cat-ob(C) {}\mrightarrow{} Type)
Date html generated:
2020_05_20-AM-07_49_30
Last ObjectModification:
2017_01_10-PM-06_15_36
Theory : small!categories
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