Nuprl Lemma : A-bind_wf3
∀[AType:⋃Val:Type.⋃n:ℕ.array{i:l}(Val;n)]
(A-bind(array-model(AType)) ∈ ⋂T,S:Type. ((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,
tunion: ⋃x:A.B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f 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,
tunion: ⋃x:A.B[x],
pi2: snd(t),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
A-bind_wf2,
tunion_wf,
nat_wf,
array_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
sqequalRule,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
instantiate,
universeEquality,
lambdaEquality,
cumulativity
Latex:
\mforall{}[AType:\mcup{}Val:Type.\mcup{}n:\mBbbN{}.array\{i:l\}(Val;n)]
(A-bind(array-model(AType)) \mmember{} \mcap{}T,S:Type. ((A-map T) {}\mrightarrow{} (T {}\mrightarrow{} (A-map S)) {}\mrightarrow{} (A-map S)))
Date html generated:
2016_05_15-PM-02_18_32
Last ObjectModification:
2015_12_27-AM-08_58_46
Theory : monads
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