Nuprl Lemma : upd_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)].  (upd(AType) ∈ ℕn ⟶ Val ⟶ Arr(AType) ⟶ Arr(AType))
Proof
Definitions occuring in Statement : 
upd: upd(AType)
, 
Arr: Arr(AType)
, 
array: array{i:l}(Val;n)
, 
int_seg: {i..j-}
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
natural_number: $n
, 
universe: Type
Definitions unfolded in proof : 
Arr: Arr(AType)
, 
array: array{i:l}(Val;n)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
upd: upd(AType)
, 
pi1: fst(t)
, 
pi2: snd(t)
, 
prop: ℙ
, 
nat: ℕ
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
int_seg: {i..j-}
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
exists: ∃x:A. B[x]
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
Lemmas referenced : 
int_seg_wf, 
uall_wf, 
equal_wf, 
eq_int_wf, 
bool_wf, 
eqff_to_assert, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
neg_assert_of_eq_int, 
nat_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
productElimination, 
thin, 
functionExtensionality, 
applyEquality, 
hypothesisEquality, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
because_Cache, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
productEquality, 
universeEquality, 
functionEquality, 
natural_numberEquality, 
setElimination, 
rename, 
lambdaEquality, 
cumulativity, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
independent_isectElimination, 
dependent_pairFormation, 
promote_hyp, 
dependent_functionElimination, 
instantiate, 
independent_functionElimination, 
voidElimination, 
isect_memberEquality
Latex:
\mforall{}[Val:Type].  \mforall{}[n:\mBbbN{}].  \mforall{}[AType:array\{i:l\}(Val;n)].
    (upd(AType)  \mmember{}  \mBbbN{}n  {}\mrightarrow{}  Val  {}\mrightarrow{}  Arr(AType)  {}\mrightarrow{}  Arr(AType))
Date html generated:
2017_10_01-AM-08_43_50
Last ObjectModification:
2017_07_26-PM-04_29_58
Theory : monads
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