Nuprl Lemma : bag-cat-monad_wf
bag-cat-monad() ∈ Monad(TypeCat)
Proof
Definitions occuring in Statement :
bag-cat-monad: bag-cat-monad(),
cat-monad: Monad(C),
type-cat: TypeCat,
member: t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
cat-ob: cat-ob(C),
pi1: fst(t),
type-cat: TypeCat,
so_apply: x[s],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
all: ∀x:A. B[x],
top: Top,
so_apply: x[s1;s2;s3],
uimplies: b supposing a,
compose: f o g,
squash: ↓T,
prop: ℙ,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
id_functor: 1,
bag-cat-monad: bag-cat-monad(),
functor-comp: functor-comp(F;G),
bag-combine: ⋃x∈bs.f[x]
Lemmas referenced :
type-cat_wf,
mk-functor_wf,
bag_wf,
subtype_rel_self,
cat-ob_wf,
cat_arrow_triple_lemma,
cat_ob_pair_lemma,
bag-map_wf,
cat-arrow_wf,
cat_comp_tuple_lemma,
bag-map-map,
compose_wf,
cat_id_tuple_lemma,
equal_wf,
squash_wf,
true_wf,
bag-map-trivial,
iff_weakening_equal,
mk-nat-trans_wf,
id_functor_wf,
ob_mk_functor_lemma,
single-bag_wf,
arrow_mk_functor_lemma,
bag_map_single_lemma,
mk-monad_wf,
functor-comp_wf,
bag-union_wf,
bag-map-union2,
ap_mk_nat_trans_lemma,
bag-union-union-as-combine,
bag-combine-single-right,
bag-union-single,
bag-subtype-list
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
introduction,
extract_by_obid,
hypothesis,
thin,
instantiate,
sqequalHypSubstitution,
isectElimination,
because_Cache,
sqequalRule,
lambdaEquality,
hypothesisEquality,
applyEquality,
universeEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
lambdaFormation,
functionExtensionality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
bag-cat-monad() \mmember{} Monad(TypeCat)
Date html generated:
2018_05_22-PM-09_58_05
Last ObjectModification:
2018_05_20-PM-10_11_02
Theory : small!categories
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