Nuprl Lemma : blended-real-agrees
∀[k:ℕ+]. ∀[x,y:ℝ]. ∀n:ℕ+k ÷ 6. ((blended-real(k;x;y) n) = (accelerate(3;x) n) ∈ ℤ)
Proof
Definitions occuring in Statement :
blended-real: blended-real(k;x;y),
accelerate: accelerate(k;f),
real: ℝ,
int_seg: {i..j-},
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
divide: n ÷ m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
accelerate: accelerate(k;f),
blended-real: blended-real(k;x;y),
blend-seq: blend-seq(k;x;y),
nat_plus: ℕ+,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
false: False,
prop: ℙ,
int_seg: {i..j-},
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
real: ℝ,
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
has-value: (a)↓,
int_nzero: ℤ-o,
subtype_rel: A ⊆r B,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b)
Lemmas referenced :
int_seg_wf,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
real_wf,
nat_plus_wf,
value-type-has-value,
int-value-type,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
int_seg_properties,
nat_plus_properties,
decidable__equal_int,
full-omega-unsat,
intformnot_wf,
intformeq_wf,
itermMultiply_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_mul_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformand_wf,
intformless_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_formula_prop_le_lemma,
less_than_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
div_rem_sum,
nequal_wf,
rem_bounds_1,
nat_plus_subtype_nat,
itermAdd_wf,
int_term_value_add_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalRule,
callbyvalueReduce,
sqleReflexivity,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
divideEquality,
setElimination,
rename,
because_Cache,
addLevel,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
baseClosed,
lambdaEquality,
hypothesisEquality,
axiomEquality,
isect_memberEquality,
multiplyEquality,
unionElimination,
equalityElimination,
productElimination,
applyEquality,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
voidEquality,
dependent_set_memberEquality,
independent_pairFormation,
promote_hyp,
imageMemberEquality,
imageElimination
Latex:
\mforall{}[k:\mBbbN{}\msupplus{}]. \mforall{}[x,y:\mBbbR{}]. \mforall{}n:\mBbbN{}\msupplus{}k \mdiv{} 6. ((blended-real(k;x;y) n) = (accelerate(3;x) n))
Date html generated:
2017_10_03-AM-10_09_12
Last ObjectModification:
2017_07_05-PM-04_40_31
Theory : reals
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