Nuprl Lemma : cat-monad_wf
∀[C:SmallCategory]. (Monad(C) ∈ Type)
Proof
Definitions occuring in Statement :
cat-monad: Monad(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
prop: ℙ,
and: P ∧ Q,
id_functor: 1,
so_apply: x[s],
so_lambda: λ2x.t[x],
so_apply: x[s1;s2;s3],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
all: ∀x:A. B[x],
functor-comp: functor-comp(F;G),
nat-trans: nat-trans(C;D;F;G),
spreadn: spread3,
member: t ∈ T,
cat-monad: Monad(C),
uall: ∀[x:A]. B[x]
Lemmas referenced :
functor-arrow_wf,
cat-id_wf,
cat-comp_wf,
functor-ob_wf,
cat-arrow_wf,
equal_wf,
cat-ob_wf,
all_wf,
arrow_mk_functor_lemma,
ob_mk_functor_lemma,
functor-comp_wf,
id_functor_wf,
nat-trans_wf,
cat-functor_wf,
small-category_wf
Rules used in proof :
functionExtensionality,
because_Cache,
applyEquality,
lambdaEquality,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
rename,
setElimination,
sqequalRule,
productElimination,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
productEquality,
hypothesis,
extract_by_obid,
introduction,
cut,
setEquality,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[C:SmallCategory]. (Monad(C) \mmember{} Type)
Date html generated:
2017_01_19-PM-02_57_46
Last ObjectModification:
2017_01_16-PM-07_38_47
Theory : small!categories
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