Nuprl Lemma : finite-function-equipollent-tuple
∀n:ℕ. ∀F:ℕn ⟶ Type. i:ℕn ⟶ F[i] ~ tuple-type(map(λi.F[i];upto(n)))
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
tuple-type: tuple-type(L),
upto: upto(n),
map: map(f;as),
int_seg: {i..j-},
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x],
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
upto: upto(n),
from-upto: [n, m),
ifthenelse: if b then t else f fi ,
lt_int: i <z j,
bfalse: ff,
top: Top,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
nat_plus: ℕ+,
subtype_rel: A ⊆r B,
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
btrue: tt
Lemmas referenced :
product_functionality_wrt_equipollent_left,
finite-function-equipollent,
null_nil_lemma,
tupletype_cons_lemma,
tuple-type-append-equipollent,
equipollent_inversion,
equipollent_functionality_wrt_equipollent2,
nil_wf,
decidable__le,
cons_wf,
lelt_wf,
int_term_value_subtract_lemma,
int_formula_prop_not_lemma,
itermSubtract_wf,
intformnot_wf,
decidable__lt,
append_wf,
map_cons_lemma,
map_append_sq,
upto_decomp1,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
intformand_wf,
satisfiable-full-omega-tt,
int_seg_properties,
equipollent-unit,
tupletype_nil_lemma,
map_nil_lemma,
nat_wf,
primrec-wf2,
less_than_wf,
set_wf,
upto_wf,
map_wf,
tuple-type_wf,
equipollent_wf,
subtract_wf,
all_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
thin,
functionEquality,
cumulativity,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
natural_numberEquality,
hypothesis,
universeEquality,
rename,
setElimination,
hypothesisEquality,
instantiate,
sqequalRule,
lambdaEquality,
applyEquality,
intEquality,
introduction,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_functionElimination,
because_Cache,
productElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
functionExtensionality,
dependent_set_memberEquality,
unionElimination,
productEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}F:\mBbbN{}n {}\mrightarrow{} Type. i:\mBbbN{}n {}\mrightarrow{} F[i] \msim{} tuple-type(map(\mlambda{}i.F[i];upto(n)))
Date html generated:
2016_05_15-PM-05_50_18
Last ObjectModification:
2016_01_16-PM-00_33_52
Theory : general
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