Nuprl Lemma : cat-comp-ident2

`∀[C:SmallCategory]. ∀x,y:cat-ob(C). ∀f:cat-arrow(C) x y.  ((cat-comp(C) x y y f (cat-id(C) y)) = f ∈ (cat-arrow(C) x y))`

Proof

Definitions occuring in Statement :  cat-comp: `cat-comp(C)` cat-id: `cat-id(C)` cat-arrow: `cat-arrow(C)` cat-ob: `cat-ob(C)` small-category: `SmallCategory` uall: `∀[x:A]. B[x]` all: `∀x:A. B[x]` apply: `f a` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` all: `∀x:A. B[x]` and: `P ∧ Q`
Lemmas referenced :  cat-comp-ident cat-arrow_wf cat-ob_wf small-category_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaFormation extract_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality dependent_functionElimination productElimination hypothesis applyEquality sqequalRule lambdaEquality axiomEquality because_Cache

Latex:
\mforall{}[C:SmallCategory].  \mforall{}x,y:cat-ob(C).  \mforall{}f:cat-arrow(C)  x  y.    ((cat-comp(C)  x  y  y  f  (cat-id(C)  y))  =  f)

Date html generated: 2020_05_20-AM-07_50_02
Last ObjectModification: 2017_01_11-PM-02_09_42

Theory : small!categories

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