Nuprl Lemma : accelerate-real-strong-regular
∀k:ℕ+. ∀x:ℝ. strong-regular-int-seq(2 * k;(2 * k) + 1;accelerate(k;x))
Proof
Definitions occuring in Statement :
accelerate: accelerate(k;f),
real: ℝ,
strong-regular-int-seq: strong-regular-int-seq(a;b;f),
nat_plus: ℕ+,
all: ∀x:A. B[x],
multiply: n * m,
add: n + m,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
strong-regular-int-seq: strong-regular-int-seq(a;b;f),
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_plus: ℕ+,
prop: ℙ,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
implies: P ⇒ Q,
regular-int-seq: k-regular-seq(f),
accelerate: accelerate(k;f),
squash: ↓T,
uimplies: b supposing a,
has-value: (a)↓,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
nequal: a ≠ b ∈ T ,
less_than: a < b,
less_than': less_than'(a;b),
int_nzero: ℤ-o,
rev_uimplies: rev_uimplies(P;Q),
ge: i ≥ j ,
le: A ≤ B,
uiff: uiff(P;Q),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
sq_stable__le,
absval_wf,
subtract_wf,
accelerate_wf,
real-regular,
regular-int-seq_wf,
nat_plus_wf,
real_wf,
value-type-has-value,
int-value-type,
subtype_base_sq,
int_subtype_base,
equal_wf,
squash_wf,
true_wf,
absval_pos,
nat_plus_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermMultiply_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
iff_weakening_equal,
intformeq_wf,
int_formula_prop_eq_lemma,
equal-wf-base,
decidable__equal_int,
itermSubtract_wf,
int_term_value_subtract_lemma,
mul_nat_plus,
less_than_wf,
nequal_wf,
rem_bounds_absval,
nat_wf,
absval_mul,
absval_nat_plus,
equal-wf-T-base,
div_rem_sum2,
itermAdd_wf,
int_term_value_add_lemma,
le_functionality,
int-triangle-inequality,
le_weakening,
mul_cancel_in_le,
multiply-is-int-iff,
add-is-int-iff,
false_wf,
set_subtype_base,
absval-non-neg,
nat_plus_subtype_nat,
add_functionality_wrt_le,
int-triangle-inequality2,
add_functionality_wrt_eq,
mul_preserves_le
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
introduction,
extract_by_obid,
isectElimination,
multiplyEquality,
natural_numberEquality,
because_Cache,
hypothesis,
applyEquality,
hypothesisEquality,
dependent_set_memberEquality,
functionExtensionality,
sqequalRule,
addEquality,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
intEquality,
independent_isectElimination,
callbyvalueReduce,
instantiate,
cumulativity,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
dependent_functionElimination,
unionElimination,
approximateComputation,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
productElimination,
baseApply,
closedConclusion,
divideEquality,
remainderEquality,
pointwiseFunctionality,
promote_hyp,
equalityUniverse,
levelHypothesis
Latex:
\mforall{}k:\mBbbN{}\msupplus{}. \mforall{}x:\mBbbR{}. strong-regular-int-seq(2 * k;(2 * k) + 1;accelerate(k;x))
Date html generated:
2017_10_02-PM-07_13_39
Last ObjectModification:
2017_09_20-PM-05_08_49
Theory : reals
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