Nuprl Lemma : A-return'_wf

[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)].
  (A-return'(array-model(AType)) ∈ ⋂T:Type. (T ⟶ (A-map'(array-model(AType)) T)))


Proof




Definitions occuring in Statement :  A-return': A-return'(AModel) A-map': A-map'(AModel) array-model: array-model(AType) array: array{i:l}(Val;n) nat: uall: [x:A]. B[x] member: t ∈ T apply: a isect: x:A. B[x] function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T array-model: array-model(AType) A-return': A-return'(AModel) A-map': A-map'(AModel) pi2: snd(t) pi1: fst(t) array-monad': array-monad'(AType) M-return: M-return(Mnd) M-map: M-map(mnd) mk_monad: mk_monad(M;return;bind)
Lemmas referenced :  array_wf nat_wf Arr_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution hypothesis sqequalRule axiomEquality equalityTransitivity equalitySymmetry lemma_by_obid isectElimination thin hypothesisEquality isect_memberEquality because_Cache universeEquality lambdaEquality

Latex:
\mforall{}[Val:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[AType:array\{i:l\}(Val;n)].
    (A-return'(array-model(AType))  \mmember{}  \mcap{}T:Type.  (T  {}\mrightarrow{}  (A-map'(array-model(AType))  T)))



Date html generated: 2016_05_15-PM-02_18_42
Last ObjectModification: 2015_12_27-AM-08_58_42

Theory : monads


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