Nuprl Lemma : idx_wf
∀[Val:Type]. ∀[n:ℕ]. ∀[AType:array{i:l}(Val;n)]. (idx(AType) ∈ ℕn ⟶ Arr(AType) ⟶ Val)
Proof
Definitions occuring in Statement :
idx: idx(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,
idx: idx(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)]. (idx(AType) \mmember{} \mBbbN{}n {}\mrightarrow{} Arr(AType) {}\mrightarrow{} Val)
Date html generated:
2017_10_01-AM-08_43_49
Last ObjectModification:
2017_07_26-PM-04_29_57
Theory : monads
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