Nuprl Lemma : M-associative
∀[Mnd:Monad]. ∀[T,S,U:Type]. ∀[m:M-map(Mnd) T]. ∀[f:T ⟶ (M-map(Mnd) S)]. ∀[g:S ⟶ (M-map(Mnd) U)].
((M-bind(Mnd) (M-bind(Mnd) m f) g) = (M-bind(Mnd) m (λx.(M-bind(Mnd) (f x) g))) ∈ (M-map(Mnd) U))
Proof
Definitions occuring in Statement :
M-bind: M-bind(Mnd),
M-map: M-map(mnd),
monad: Monad,
uall: ∀[x:A]. B[x],
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
monad: Monad,
M-bind: M-bind(Mnd),
M-map: M-map(mnd),
pi1: fst(t),
pi2: snd(t)
Lemmas referenced :
M-map_wf,
monad_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
hypothesis,
functionIsType,
universeIsType,
hypothesisEquality,
applyEquality,
extract_by_obid,
isectElimination,
isect_memberEquality,
axiomEquality,
functionEquality,
because_Cache,
inhabitedIsType,
universeEquality
Latex:
\mforall{}[Mnd:Monad]. \mforall{}[T,S,U:Type]. \mforall{}[m:M-map(Mnd) T]. \mforall{}[f:T {}\mrightarrow{} (M-map(Mnd) S)]. \mforall{}[g:S {}\mrightarrow{} (M-map(Mnd) U)].
((M-bind(Mnd) (M-bind(Mnd) m f) g) = (M-bind(Mnd) m (\mlambda{}x.(M-bind(Mnd) (f x) g))))
Date html generated:
2019_10_15-AM-10_59_21
Last ObjectModification:
2018_09_27-AM-11_06_11
Theory : monads
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