Nuprl Lemma : i-approx_wf
∀[n:ℕ+]. ∀[I:Interval]. (i-approx(I;n) ∈ Interval)
Proof
Definitions occuring in Statement :
i-approx: i-approx(I;n),
interval: Interval,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
i-approx: i-approx(I;n),
interval: Interval,
nat_plus: ℕ+,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
nat_plus_wf,
interval_wf,
radd_wf,
rless_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_plus_properties,
rless-int,
int-to-real_wf,
rdiv_wf,
rsub_wf,
rccint_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
productElimination,
thin,
unionElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
because_Cache,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
inrFormation,
dependent_functionElimination,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
minusEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[I:Interval]. (i-approx(I;n) \mmember{} Interval)
Date html generated:
2016_05_18-AM-08_39_25
Last ObjectModification:
2016_01_17-AM-02_23_35
Theory : reals
Home
Index