Nuprl Lemma : monad-from_wf
∀[Mnd:Monad]. (monad-from(Mnd) ∈ Monad(TypeCat))
Proof
Definitions occuring in Statement : 
monad-from: monad-from(Mnd)
, 
monad: Monad
, 
cat-monad: Monad(C)
, 
type-cat: TypeCat
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
implies: P 
⇒ Q
, 
monad-from: monad-from(Mnd)
, 
uimplies: b supposing a
, 
type-cat: TypeCat
, 
top: Top
, 
so_lambda: so_lambda3, 
so_apply: x[s1;s2;s3]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
compose: f o g
, 
cat-ob: cat-ob(C)
, 
pi1: fst(t)
, 
cat-arrow: cat-arrow(C)
, 
pi2: snd(t)
, 
squash: ↓T
, 
prop: ℙ
, 
true: True
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
M-return: M-return(Mnd)
, 
id_functor: 1
, 
nat-trans: nat-trans(C;D;F;G)
, 
functor-comp: functor-comp(F;G)
Lemmas referenced : 
M-map_wf, 
M-bind_wf, 
istype-universe, 
mk-monad_wf, 
cat_ob_pair_lemma, 
istype-void, 
cat_arrow_triple_lemma, 
ob_mk_functor_lemma, 
cat_comp_tuple_lemma, 
arrow_mk_functor_lemma, 
cat_id_tuple_lemma, 
monad_wf, 
type-cat_wf, 
subtype_rel_self, 
cat-ob_wf, 
cat-arrow_wf, 
mk-functor_wf, 
M-return_wf, 
equal_wf, 
squash_wf, 
true_wf, 
trivial-equal, 
M-associative, 
iff_weakening_equal, 
M-leftunit, 
M-rightunit, 
eta_conv, 
compose_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
cut, 
lambdaEquality_alt, 
lambdaFormation_alt, 
applyEquality, 
hypothesisEquality, 
universeIsType, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
functionIsType, 
inhabitedIsType, 
because_Cache, 
dependent_functionElimination, 
equalityTransitivity, 
equalitySymmetry, 
equalityIsType1, 
independent_functionElimination, 
sqequalRule, 
instantiate, 
universeEquality, 
independent_isectElimination, 
isect_memberEquality_alt, 
voidElimination, 
functionExtensionality, 
functionEquality, 
imageElimination, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed, 
productElimination, 
hyp_replacement, 
applyLambdaEquality, 
dependent_set_memberEquality_alt, 
cumulativity, 
lambdaFormation, 
isectEquality, 
lambdaEquality
Latex:
\mforall{}[Mnd:Monad].  (monad-from(Mnd)  \mmember{}  Monad(TypeCat))
Date html generated:
2020_05_20-AM-08_04_16
Last ObjectModification:
2020_01_16-PM-05_25_21
Theory : bags
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