Nuprl Lemma : cat-cat_wf
Cat ∈ SmallCategory'
Proof
Definitions occuring in Statement :
cat-cat: Cat,
small-category: SmallCategory,
member: t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
small-category: SmallCategory,
cat-cat: Cat,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
uimplies: b supposing a,
true: True,
prop: ℙ,
squash: ↓T,
all: ∀x:A. B[x],
cand: A c∧ B,
and: P ∧ Q,
spreadn: spread4
Lemmas referenced :
small-category_wf,
cat-functor_wf,
subtype_rel_universe1,
id_functor_wf,
functor-comp_wf,
iff_weakening_equal,
functor-comp-assoc,
true_wf,
squash_wf,
equal_wf,
functor-comp-id
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_set_memberEquality_alt,
dependent_pairEquality_alt,
cut,
introduction,
extract_by_obid,
hypothesis,
lambdaEquality_alt,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
sqequalRule,
inhabitedIsType,
because_Cache,
productIsType,
functionIsType,
universeIsType,
independent_pairEquality,
independent_functionElimination,
independent_isectElimination,
baseClosed,
imageMemberEquality,
natural_numberEquality,
universeEquality,
equalitySymmetry,
equalityTransitivity,
imageElimination,
lambdaEquality,
independent_pairFormation,
productElimination,
lambdaFormation,
equalityIsType1
Latex:
Cat \mmember{} SmallCategory'
Date html generated:
2020_05_20-AM-07_53_46
Last ObjectModification:
2018_11_10-AM-11_32_33
Theory : small!categories
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