Nuprl Lemma : qlog_wf
∀e:{e:ℚ| 0 < e} . ∀q:{q:ℚ| (0 ≤ q) ∧ q < 1} . (qlog(q;e) ∈ qlog-type(q;e))
Proof
Definitions occuring in Statement :
qlog-type: qlog-type(q;e),
qlog: qlog(q;e),
qle: r ≤ s,
qless: r < s,
rationals: ℚ,
all: ∀x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
set: {x:A| B[x]} ,
natural_number: $n
Definitions unfolded in proof :
qlog-type: qlog-type(q;e),
all: ∀x:A. B[x],
member: t ∈ T,
qlog: qlog(q;e),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
nat: ℕ,
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
cand: A c∧ B,
so_apply: x[s]
Lemmas referenced :
qlog-ext,
subtype_rel_self,
rationals_wf,
qless_wf,
all_wf,
qle_wf,
set_wf,
nat_plus_wf,
qexp_wf,
subtract_wf,
nat_plus_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_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_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
nat_plus_subtype_nat,
int-subtype-rationals
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
setElimination,
thin,
rename,
applyEquality,
instantiate,
extract_by_obid,
hypothesis,
introduction,
sqequalHypSubstitution,
isectElimination,
functionEquality,
setEquality,
natural_numberEquality,
because_Cache,
hypothesisEquality,
productEquality,
lambdaEquality,
productElimination,
dependent_set_memberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation
Latex:
\mforall{}e:\{e:\mBbbQ{}| 0 < e\} . \mforall{}q:\{q:\mBbbQ{}| (0 \mleq{} q) \mwedge{} q < 1\} . (qlog(q;e) \mmember{} qlog-type(q;e))
Date html generated:
2018_05_22-AM-00_14_24
Last ObjectModification:
2018_05_19-PM-04_05_44
Theory : rationals
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