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 :
uall: ∀[x:A]. B[x],
cat-monad: Monad(C),
member: t ∈ T,
spreadn: spread3,
nat-trans: nat-trans(C;D;F;G),
functor-comp: functor-comp(F;G),
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],
id_functor: 1,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
small-category_wf,
cat-functor_wf,
nat-trans_wf,
id_functor_wf,
functor-comp_wf,
ob_mk_functor_lemma,
arrow_mk_functor_lemma,
all_wf,
cat-ob_wf,
equal_wf,
cat-arrow_wf,
functor-ob_wf,
cat-comp_wf,
cat-id_wf,
functor-arrow_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
setEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
productEquality,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
sqequalRule,
setElimination,
rename,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaEquality,
applyEquality,
because_Cache,
functionExtensionality
Latex:
\mforall{}[C:SmallCategory]. (Monad(C) \mmember{} Type)
Date html generated:
2020_05_20-AM-07_58_27
Last ObjectModification:
2017_01_16-PM-07_38_47
Theory : small!categories
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