### Nuprl Lemma : cat-inverse_wf

`∀[C:SmallCategory]. ∀[x,y:cat-ob(C)]. ∀[f:cat-arrow(C) x y]. ∀[g:cat-arrow(C) y x].  (fg=1 ∈ ℙ)`

Proof

Definitions occuring in Statement :  cat-inverse: `fg=1` 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-inverse: `fg=1`
Lemmas referenced :  equal_wf cat-arrow_wf cat-comp_wf cat-id_wf cat-ob_wf small-category_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin applyEquality hypothesisEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache

Latex:
\mforall{}[C:SmallCategory].  \mforall{}[x,y:cat-ob(C)].  \mforall{}[f:cat-arrow(C)  x  y].  \mforall{}[g:cat-arrow(C)  y  x].    (fg=1  \mmember{}  \mBbbP{})

Date html generated: 2020_05_20-AM-07_49_50
Last ObjectModification: 2017_01_08-PM-00_30_55

Theory : small!categories

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