Nuprl Lemma : A-leftunit'

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


Proof




Definitions occuring in Statement :  A-bind': A-bind'(AModel) 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] apply: a function: x:A ⟶ B[x] universe: Type equal: t ∈ T
Definitions unfolded in proof :  array-model: array-model(AType) A-return': A-return'(AModel) A-bind': A-bind'(AModel) A-map': A-map'(AModel) pi2: snd(t) pi1: fst(t) uall: [x:A]. B[x] member: t ∈ T squash: T prop: true: True subtype_rel: A ⊆B uimplies: supposing a guard: {T} iff: ⇐⇒ Q and: P ∧ Q rev_implies:  Q implies:  Q
Lemmas referenced :  equal_wf squash_wf true_wf M-map_wf array-monad'_wf M-leftunit iff_weakening_equal array_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut applyEquality thin lambdaEquality sqequalHypSubstitution imageElimination extract_by_obid isectElimination hypothesisEquality equalityTransitivity hypothesis equalitySymmetry universeEquality cumulativity functionExtensionality natural_numberEquality imageMemberEquality baseClosed independent_isectElimination productElimination independent_functionElimination because_Cache functionEquality isect_memberEquality axiomEquality

Latex:
\mforall{}[Val:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[AType:array\{i:l\}(Val;n)].  \mforall{}[T,S:Type].  \mforall{}[x:T].
\mforall{}[f:T  {}\mrightarrow{}  (A-map'(array-model(AType))  S)].
    ((A-bind'(array-model(AType))  (A-return'(array-model(AType))  x)  f)  =  (f  x))



Date html generated: 2017_10_01-AM-08_44_06
Last ObjectModification: 2017_07_26-PM-04_30_07

Theory : monads


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