Nuprl Lemma : approx-rexp_wf
∀[x:ℝ]. ∀[n:ℕ]. (approx-rexp(x;n) ∈ ℝ)
Proof
Definitions occuring in Statement :
approx-rexp: approx-rexp(x;n),
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
approx-rexp: approx-rexp(x;n),
real: ℝ,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
and: P ∧ Q,
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
prop: ℙ,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
has-value: (a)↓,
top: Top,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
divide_wfa,
istype-less_than,
subtype_base_sq,
int_subtype_base,
istype-int,
nequal_wf,
decidable__equal_int,
int-to-real_wf,
value-type-has-value,
int-value-type,
decidable__lt,
istype-top,
istype-void,
less_than_wf,
istype-nat,
real_wf,
subtract_wf,
nat_properties,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermMultiply_wf,
itermVar_wf,
intformeq_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
rational-approx_wf,
rexp_wf,
int-rdiv_wf,
decidable__le,
exp-fastexp,
istype-le,
exp_wf_nat_plus,
subtype_rel_sets_simple,
le_wf,
nat_plus_properties,
int_upper_wf,
set-value-type,
mul_nat_plus,
int_upper_properties,
mul_nzero,
int_entire_a
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
addEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
setElimination,
rename,
because_Cache,
hypothesis,
dependent_set_memberEquality_alt,
closedConclusion,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
imageMemberEquality,
hypothesisEquality,
baseClosed,
lambdaFormation_alt,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
voidElimination,
equalityIstype,
sqequalBase,
universeIsType,
inhabitedIsType,
unionElimination,
int_eqReduceFalseSq,
callbyvalueReduce,
lessCases,
axiomSqEquality,
isect_memberEquality_alt,
isectIsTypeImplies,
imageElimination,
productElimination,
axiomEquality,
multiplyEquality,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
baseApply,
applyLambdaEquality
Latex:
\mforall{}[x:\mBbbR{}]. \mforall{}[n:\mBbbN{}]. (approx-rexp(x;n) \mmember{} \mBbbR{})
Date html generated:
2019_10_31-AM-06_10_57
Last ObjectModification:
2019_04_03-PM-02_22_11
Theory : reals_2
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