Nuprl Lemma : accelerate-bdd-diff
∀k:ℕ+. ∀[f:{f:ℕ+ ⟶ ℤ| k-regular-seq(f)} ]. bdd-diff(accelerate(k;f);f)
Proof
Definitions occuring in Statement :
accelerate: accelerate(k;f),
bdd-diff: bdd-diff(f;g),
regular-int-seq: k-regular-seq(f),
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
bdd-diff: bdd-diff(f;g),
exists: ∃x:A. B[x],
member: t ∈ T,
nat: ℕ,
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
squash: ↓T,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
le: A ≤ B,
accelerate: accelerate(k;f),
has-value: (a)↓,
less_than: a < b,
less_than': less_than'(a;b),
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
rev_uimplies: rev_uimplies(P;Q),
ge: i ≥ j ,
subtract: n - m,
regular-int-seq: k-regular-seq(f),
sq_stable: SqStable(P)
Lemmas referenced :
left_mul_subtract_distrib,
nat_plus_subtype_nat,
sq_stable__le,
rem_bounds_absval_le,
add_functionality_wrt_le,
absval_sym,
add_functionality_wrt_eq,
add-commutes,
minus-one-mul,
add-associates,
mul-associates,
int-triangle-inequality,
le_weakening,
le_functionality,
nequal_wf,
mul_nat_plus,
div_rem_sum2,
int-value-type,
value-type-has-value,
regular-int-seq_wf,
set_wf,
all_wf,
nat_plus_wf,
less_than'_wf,
int_term_value_subtract_lemma,
itermSubtract_wf,
decidable__equal_int,
subtype_base_sq,
less_than_wf,
set_subtype_base,
int_subtype_base,
absval_pos,
iff_weakening_equal,
nat_wf,
absval_mul,
true_wf,
squash_wf,
equal_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
absval_nat_plus,
accelerate_wf,
subtract_wf,
absval_wf,
mul_cancel_in_le,
le_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_mul_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermMultiply_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_plus_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
isect_memberFormation,
dependent_pairFormation,
dependent_set_memberEquality,
addEquality,
multiplyEquality,
natural_numberEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
hypothesisEquality,
cut,
lemma_by_obid,
isectElimination,
hypothesis,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
introduction,
applyEquality,
because_Cache,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
independent_functionElimination,
sqequalIntensionalEquality,
baseApply,
closedConclusion,
instantiate,
independent_pairEquality,
axiomEquality,
functionEquality,
callbyvalueReduce,
remainderEquality,
minusEquality,
cumulativity
Latex:
\mforall{}k:\mBbbN{}\msupplus{}. \mforall{}[f:\{f:\mBbbN{}\msupplus{} {}\mrightarrow{} \mBbbZ{}| k-regular-seq(f)\} ]. bdd-diff(accelerate(k;f);f)
Date html generated:
2016_05_18-AM-06_47_19
Last ObjectModification:
2016_01_17-AM-01_45_52
Theory : reals
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