### Nuprl Lemma : functor_arrow_wf

`∀[C,D:SmallCategory]. ∀[F:Functor(C;D)]. ∀[x,y:cat-ob(C)]. ∀[f:cat-arrow(C) x y].`
`  (F(f) ∈ cat-arrow(D) (ob(F) x) (ob(F) y))`

Proof

Definitions occuring in Statement :  functor_arrow: `F(f)` functor-ob: `ob(F)` cat-functor: `Functor(C1;C2)` cat-arrow: `cat-arrow(C)` cat-ob: `cat-ob(C)` small-category: `SmallCategory` uall: `∀[x:A]. B[x]` member: `t ∈ T` apply: `f a`
Definitions unfolded in proof :  functor_arrow: `F(f)` member: `t ∈ T` uall: `∀[x:A]. B[x]`
Lemmas referenced :  small-category_wf cat-functor_wf cat-ob_wf cat-arrow_wf functor-arrow_wf
Rules used in proof :  because_Cache isect_memberEquality equalitySymmetry equalityTransitivity axiomEquality hypothesis hypothesisEquality thin isectElimination sqequalHypSubstitution extract_by_obid applyEquality sqequalRule cut introduction isect_memberFormation sqequalReflexivity computationStep sqequalTransitivity sqequalSubstitution

Latex:
\mforall{}[C,D:SmallCategory].  \mforall{}[F:Functor(C;D)].  \mforall{}[x,y:cat-ob(C)].  \mforall{}[f:cat-arrow(C)  x  y].
(F(f)  \mmember{}  cat-arrow(D)  (ob(F)  x)  (ob(F)  y))

Date html generated: 2017_01_19-PM-02_52_25
Last ObjectModification: 2017_01_17-PM-00_44_46

Theory : small!categories

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