Nuprl Lemma : op-cat_wf
∀[C:SmallCategory]. (op-cat(C) ∈ SmallCategory)
Proof
Definitions occuring in Statement :
op-cat: op-cat(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
op-cat: op-cat(C),
small-category: SmallCategory,
spreadn: spread4,
and: P ∧ Q,
subtype_rel: A ⊆r B,
cand: A c∧ B,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
true: True,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
iff_weakening_equal,
all_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
dependent_set_memberEquality,
dependent_pairEquality,
cumulativity,
hypothesisEquality,
lambdaEquality,
applyEquality,
functionExtensionality,
because_Cache,
independent_pairEquality,
hypothesis,
productEquality,
functionEquality,
universeEquality,
lambdaFormation,
independent_pairFormation,
imageElimination,
extract_by_obid,
isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[C:SmallCategory]. (op-cat(C) \mmember{} SmallCategory)
Date html generated:
2020_05_20-AM-07_52_05
Last ObjectModification:
2017_07_28-AM-09_19_28
Theory : small!categories
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