Nuprl Lemma : logseq_wf
∀[a:{a:ℝ| r0 < a} ]. ∀[b:ℝ]. ∀[n:ℕ]. (logseq(a;b;n) ∈ ℝ)
Proof
Definitions occuring in Statement :
logseq: logseq(a;b;n),
rless: x < y,
int-to-real: r(n),
real: ℝ,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
int_seg: {i..j-},
guard: {T},
rless: x < y,
sq_exists: ∃x:{A| B[x]},
lelt: i ≤ j < k,
sq_stable: SqStable(P),
squash: ↓T,
nat_plus: ℕ+,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
real: ℝ,
less_than: a < b,
true: True,
int_nzero: ℤ-o,
nequal: a ≠ b ∈ T ,
sq_type: SQType(T),
logseq: logseq(a;b;n),
has-value: (a)↓,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exp-fastexp,
exp_wf4,
false_wf,
int_seg_properties,
nat_properties,
sq_stable__less_than,
nat_plus_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
value-type-has-value,
exp_wf2,
mul_nat_plus,
exp_wf_nat_plus,
less_than_wf,
int_entire_a,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
mul_nzero,
equal_wf,
exp_wf3,
nequal_wf,
primrec_wf,
real_wf,
int-value-type,
rational-approx_wf,
log-contraction_wf,
int-rdiv_wf,
int-to-real_wf,
int_seg_wf,
nat_wf,
set_wf,
rless_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
thin,
natural_numberEquality,
because_Cache,
hypothesis,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
addEquality,
setElimination,
rename,
hypothesisEquality,
productElimination,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
multiplyEquality,
applyEquality,
addLevel,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
isect_memberFormation,
callbyvalueReduce,
axiomEquality
Latex:
\mforall{}[a:\{a:\mBbbR{}| r0 < a\} ]. \mforall{}[b:\mBbbR{}]. \mforall{}[n:\mBbbN{}]. (logseq(a;b;n) \mmember{} \mBbbR{})
Date html generated:
2016_10_26-PM-00_36_30
Last ObjectModification:
2016_09_19-AM-10_09_41
Theory : reals_2
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