Nuprl Lemma : A-eval_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. (A-eval(array-model(AType)) ∈ ⋂T:Type. ((A-map T) ⟶ Arr(AType) ⟶ T))
Proof
Definitions occuring in Statement :
A-map: A-map,
array-model: array-model(AType),
Arr: Arr(AType),
array: array{i:l}(Val;n),
A-eval: A-eval(AModel),
nat: ℕ,
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,
array-model: array-model(AType),
A-map: A-map,
pi2: snd(t),
pi1: fst(t),
array-monad: array-monad(AType),
M-map: M-map(mnd),
mk_monad: mk_monad(M;return;bind),
array: array{i:l}(Val;n),
A-eval: A-eval(AModel),
Arr: Arr(AType),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
array_wf,
nat_wf,
equal_wf,
pi1_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
extract_by_obid,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
isect_memberEquality,
because_Cache,
universeEquality,
productElimination,
lambdaFormation,
instantiate,
dependent_functionElimination,
independent_functionElimination,
lambdaEquality,
applyEquality,
functionExtensionality,
productEquality,
independent_pairEquality,
functionEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[AType:array\{i:l\}(Val;n)].
(A-eval(array-model(AType)) \mmember{} \mcap{}T:Type. ((A-map T) {}\mrightarrow{} Arr(AType) {}\mrightarrow{} T))
Date html generated:
2017_10_01-AM-08_44_01
Last ObjectModification:
2017_07_26-PM-04_30_04
Theory : monads
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