Nuprl Lemma : cat-retraction_wf

[C:SmallCategory]. ∀[x,y:cat-ob(C)]. ∀[g:cat-arrow(C) x].  (retraction(g) ∈ ℙ)


Proof




Definitions occuring in Statement :  cat-retraction: retraction(g) cat-arrow: cat-arrow(C) cat-ob: cat-ob(C) small-category: SmallCategory uall: [x:A]. B[x] prop: member: t ∈ T apply: a
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T cat-retraction: retraction(g) so_lambda: λ2x.t[x] so_apply: x[s]
Lemmas referenced :  exists_wf cat-arrow_wf cat-inverse_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 lambdaEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache

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



Date html generated: 2020_05_20-AM-07_49_55
Last ObjectModification: 2017_01_08-PM-00_35_19

Theory : small!categories


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