### Nuprl Lemma : cat-monic_wf

`∀[C:SmallCategory]. ∀[y,z:cat-ob(C)]. ∀[f:cat-arrow(C) y z].  (monic(f) ∈ ℙ)`

Proof

Definitions occuring in Statement :  cat-monic: `monic(f)` cat-arrow: `cat-arrow(C)` cat-ob: `cat-ob(C)` small-category: `SmallCategory` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` apply: `f a`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` cat-monic: `monic(f)` so_lambda: `λ2x.t[x]` uimplies: `b supposing a` prop: `ℙ` so_apply: `x[s]`
Lemmas referenced :  uall_wf cat-ob_wf cat-arrow_wf isect_wf equal_wf cat-comp_wf small-category_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis lambdaEquality applyEquality because_Cache axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality

Latex:
\mforall{}[C:SmallCategory].  \mforall{}[y,z:cat-ob(C)].  \mforall{}[f:cat-arrow(C)  y  z].    (monic(f)  \mmember{}  \mBbbP{})

Date html generated: 2017_10_05-AM-00_45_47
Last ObjectModification: 2017_07_28-AM-09_19_06

Theory : small!categories

Home Index