Nuprl Lemma : A-associative'
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. ∀[T,S,U:Type]. ∀[m:A-map'(array-model(AType)) T].
∀[f:T ⟶ (A-map'(array-model(AType)) S)]. ∀[g:S ⟶ (A-map'(array-model(AType)) U)].
  ((A-bind'(array-model(AType)) (A-bind'(array-model(AType)) m f) g)
  = (A-bind'(array-model(AType)) m (λx.(A-bind'(array-model(AType)) (f x) g)))
  ∈ (A-map'(array-model(AType)) U))
Proof
Definitions occuring in Statement : 
A-bind': A-bind'(AModel)
, 
A-map': A-map'(AModel)
, 
array-model: array-model(AType)
, 
array: array{i:l}(Val;n)
, 
nat: ℕ
, 
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 : 
array-model: array-model(AType)
, 
A-bind': A-bind'(AModel)
, 
A-map': A-map'(AModel)
, 
pi2: snd(t)
, 
pi1: fst(t)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Lemmas referenced : 
M-associative, 
M-map_wf, 
array-monad'_wf, 
array_wf, 
nat_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
because_Cache, 
hypothesis, 
functionEquality, 
hypothesisEquality, 
applyEquality, 
isect_memberEquality, 
axiomEquality, 
universeEquality
Latex:
\mforall{}[Val:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[AType:array\{i:l\}(Val;n)].  \mforall{}[T,S,U:Type].  \mforall{}[m:A-map'(array-model(AType))  T].
\mforall{}[f:T  {}\mrightarrow{}  (A-map'(array-model(AType))  S)].  \mforall{}[g:S  {}\mrightarrow{}  (A-map'(array-model(AType))  U)].
    ((A-bind'(array-model(AType))  (A-bind'(array-model(AType))  m  f)  g)
    =  (A-bind'(array-model(AType))  m  (\mlambda{}x.(A-bind'(array-model(AType))  (f  x)  g))))
Date html generated:
2016_05_15-PM-02_19_07
Last ObjectModification:
2015_12_27-AM-08_59_34
Theory : monads
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