Nuprl Lemma : A-rightunit

Val:Type. ∀n:ℕ. ∀AType:array{i:l}(Val;n). ∀T:Type. ∀m:A-map T.
  ((A-bind(array-model(AType)) A-return(array-model(AType))) m ∈ (A-map T))


Proof




Definitions occuring in Statement :  A-bind: A-bind(AModel) A-map: A-map array-model: array-model(AType) array: array{i:l}(Val;n) A-return: A-return(AModel) nat: all: x:A. B[x] apply: a 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 pi2: snd(t) pi1: fst(t) all: x:A. B[x] member: t ∈ T squash: T uall: [x:A]. B[x] 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-rightunit iff_weakening_equal array_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep lambdaFormation cut applyEquality thin lambdaEquality sqequalHypSubstitution imageElimination introduction extract_by_obid isectElimination hypothesisEquality equalityTransitivity hypothesis equalitySymmetry universeEquality cumulativity because_Cache natural_numberEquality imageMemberEquality baseClosed independent_isectElimination productElimination independent_functionElimination

Latex:
\mforall{}Val:Type.  \mforall{}n:\mBbbN{}.  \mforall{}AType:array\{i:l\}(Val;n).  \mforall{}T:Type.  \mforall{}m:A-map  T.
    ((A-bind(array-model(AType))  m  A-return(array-model(AType)))  =  m)



Date html generated: 2017_10_01-AM-08_44_07
Last ObjectModification: 2017_07_26-PM-04_30_08

Theory : monads


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