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)) f) g)
  (A-bind'(array-model(AType)) x.(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: uall: [x:A]. B[x] apply: a lambda: λx.A[x] function: x:A ⟶ B[x] universe: Type equal: 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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