Nuprl Lemma : A-bind_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. ∀[T,S:Type].
(A-bind(array-model(AType)) ∈ (A-map T) ⟶ (T ⟶ (A-map S)) ⟶ (A-map S))
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],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
array-model: array-model(AType),
A-bind: A-bind(AModel),
A-map: A-map,
pi2: snd(t),
pi1: fst(t),
array-monad: array-monad(AType),
M-bind: M-bind(Mnd),
M-map: M-map(mnd),
let: let,
mk_monad: mk_monad(M;return;bind),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
array_wf,
nat_wf,
pi1_wf,
Arr_wf,
pi2_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
universeEquality,
because_Cache,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
lambdaEquality,
applyEquality,
functionEquality,
productEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)]. \mforall{}[T,S:Type].
(A-bind(array-model(AType)) \mmember{} (A-map T) {}\mrightarrow{} (T {}\mrightarrow{} (A-map S)) {}\mrightarrow{} (A-map S))
Date html generated:
2016_05_15-PM-02_18_28
Last ObjectModification:
2015_12_27-AM-08_58_51
Theory : monads
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