Nuprl Lemma : blended-real_wf
∀[k:ℕ+]. ∀[x,y:ℝ]. blended-real(k;x;y) ∈ ℝ supposing |x - y| ≤ (r1/r(k))
Proof
Definitions occuring in Statement :
blended-real: blended-real(k;x;y),
rdiv: (x/y),
rleq: x ≤ y,
rabs: |x|,
rsub: x - y,
int-to-real: r(n),
real: ℝ,
nat_plus: ℕ+,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
blended-real: blended-real(k;x;y),
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
prop: ℙ,
real: ℝ,
implies: P ⇒ Q,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top
Lemmas referenced :
accelerate_wf,
less_than_wf,
blend-seq_wf,
blend-close-reals,
regular-int-seq_wf,
nat_plus_wf,
rleq_wf,
rabs_wf,
rsub_wf,
rdiv_wf,
int-to-real_wf,
rless-int,
nat_plus_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
rless_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
imageMemberEquality,
hypothesisEquality,
baseClosed,
hypothesis,
setElimination,
rename,
independent_functionElimination,
functionExtensionality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
independent_isectElimination,
inrFormation,
dependent_functionElimination,
productElimination,
unionElimination,
approximateComputation,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[k:\mBbbN{}\msupplus{}]. \mforall{}[x,y:\mBbbR{}]. blended-real(k;x;y) \mmember{} \mBbbR{} supposing |x - y| \mleq{} (r1/r(k))
Date html generated:
2017_10_03-AM-10_08_42
Last ObjectModification:
2017_07_05-PM-04_12_50
Theory : reals
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