Nuprl Lemma : array-model_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)].  (array-model(AType) ∈ array-model-type{i:l}(AType;Val;n))
Proof
Definitions occuring in Statement : 
array-model: array-model(AType)
, 
array-model-type: array-model-type{i:l}(AType;Val;n)
, 
array: array{i:l}(Val;n)
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
array-model: array-model(AType)
, 
array-model-type: array-model-type{i:l}(AType;Val;n)
, 
let: let, 
subtype_rel: A ⊆r B
, 
M-map: M-map(mnd)
, 
pi1: fst(t)
, 
array-monad: array-monad(AType)
, 
mk_monad: mk_monad(M;return;bind)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
prop: ℙ
, 
nat: ℕ
, 
array-monad': array-monad'(AType)
Lemmas referenced : 
M-return_wf, 
array-monad_wf, 
M-bind_wf, 
subtype_rel_self, 
Arr_wf, 
newarray_wf, 
pi1_wf, 
equal_wf, 
M-map_wf, 
it_wf, 
upd_wf, 
unit_wf2, 
int_seg_wf, 
array-monad'_wf, 
idx_wf, 
array_wf, 
nat_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
independent_pairEquality, 
isect_memberEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
cumulativity, 
hypothesisEquality, 
hypothesis, 
applyEquality, 
because_Cache, 
universeEquality, 
lambdaEquality, 
functionEquality, 
productEquality, 
lambdaFormation, 
productElimination, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination, 
natural_numberEquality, 
setElimination, 
rename, 
isectEquality, 
instantiate, 
functionExtensionality, 
axiomEquality
Latex:
\mforall{}[Val:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[AType:array\{i:l\}(Val;n)].
    (array-model(AType)  \mmember{}  array-model-type\{i:l\}(AType;Val;n))
Date html generated:
2017_10_01-AM-08_43_58
Last ObjectModification:
2017_07_26-PM-04_30_02
Theory : monads
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