Nuprl Lemma : fn_array_wf
∀[Val:Type]. ∀[n:ℕ]. (fn_array{i:l}(Val;n) ∈ array{i:l}(Val;n))
Proof
Definitions occuring in Statement :
fn_array: fn_array{i:l}(Val;n),
array: array{i:l}(Val;n),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
fn_array: fn_array{i:l}(Val;n),
array: array{i:l}(Val;n),
uall: ∀[x:A]. B[x],
member: t ∈ T,
mk_array: mk_array(Arr;idx;upd;newarray),
nat: ℕ,
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,
exposed-it: exposed-it,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False
Lemmas referenced :
int_seg_wf,
istype-universe,
eq_int_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
set_subtype_base,
lelt_wf,
istype-int,
int_subtype_base,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
ifthenelse_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
dependent_pairEquality_alt,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
natural_numberEquality,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
lambdaEquality_alt,
applyEquality,
functionIsType,
inhabitedIsType,
universeIsType,
lambdaFormation_alt,
unionElimination,
equalityElimination,
equalityIsType1,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
independent_pairEquality,
isect_memberEquality_alt,
axiomEquality,
productElimination,
independent_isectElimination,
dependent_pairFormation_alt,
equalityIsType2,
baseApply,
baseClosed,
intEquality,
promote_hyp,
instantiate,
cumulativity,
voidElimination,
productIsType,
isectIsType,
universeEquality
Latex:
\mforall{}[Val:Type]. \mforall{}[n:\mBbbN{}]. (fn\_array\{i:l\}(Val;n) \mmember{} array\{i:l\}(Val;n))
Date html generated:
2019_10_15-AM-10_59_29
Last ObjectModification:
2018_10_11-PM-06_55_12
Theory : monads
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