`∀[C:SmallCategory]. ∀[M:Monad(C)]. ∀[x:cat-ob(C)].  (monad-op(M;x) ∈ cat-arrow(C) M(M(x)) M(x))`

Proof

Definitions occuring in Statement :  monad-op: `monad-op(M;x)` monad-fun: `M(x)` cat-monad: `Monad(C)` 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 :  uall: `∀[x:A]. B[x]` member: `t ∈ T` monad-op: `monad-op(M;x)` cat-monad: `Monad(C)` nat-trans: `nat-trans(C;D;F;G)` monad-fun: `M(x)` pi2: `snd(t)` monad-functor: `monad-functor(M)` pi1: `fst(t)` id_functor: `1` all: `∀x:A. B[x]` top: `Top` so_lambda: so_lambda3 so_apply: `x[s1;s2;s3]` so_lambda: `λ2x.t[x]` so_apply: `x[s]` subtype_rel: `A ⊆r B` uimplies: `b supposing a` functor-ob: `ob(F)` functor-comp: `functor-comp(F;G)` mk-functor: mk-functor
Lemmas referenced :  ob_mk_functor_lemma arrow_mk_functor_lemma subtype_rel-equal cat-arrow_wf functor-ob_wf functor-comp_wf cat-ob_wf cat-monad_wf small-category_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule sqequalHypSubstitution setElimination thin rename productElimination extract_by_obid dependent_functionElimination isect_memberEquality voidElimination voidEquality hypothesis applyEquality hypothesisEquality isectElimination independent_isectElimination because_Cache axiomEquality equalityTransitivity equalitySymmetry

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