Nuprl Lemma : nat-trans_wf
∀[C,D:SmallCategory]. ∀[F,G:Functor(C;D)]. (nat-trans(C;D;F;G) ∈ Type)
Proof
Definitions occuring in Statement :
nat-trans: nat-trans(C;D;F;G),
cat-functor: Functor(C1;C2),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s],
so_lambda: λ2x.t[x],
nat-trans: nat-trans(C;D;F;G),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
small-category_wf,
cat-functor_wf,
functor-arrow_wf,
cat-comp_wf,
equal_wf,
all_wf,
functor-ob_wf,
cat-arrow_wf,
cat-ob_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
lambdaEquality,
because_Cache,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
functionEquality,
setEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[C,D:SmallCategory]. \mforall{}[F,G:Functor(C;D)]. (nat-trans(C;D;F;G) \mmember{} Type)
Date html generated:
2020_05_20-AM-07_51_15
Last ObjectModification:
2015_12_28-PM-02_24_13
Theory : small!categories
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