Nuprl Lemma : A-associative
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. ∀[T,S,U:Type]. ∀[m:A-map T]. ∀[f:T ⟶ (A-map S)]. ∀[g:S ⟶ (A-map 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 U))
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),
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,
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 T]. \mforall{}[f:T {}\mrightarrow{} (A-map S)].
\mforall{}[g:S {}\mrightarrow{} (A-map 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_05
Last ObjectModification:
2015_12_27-AM-08_59_35
Theory : monads
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