Nuprl Lemma : cheap-real-upper-bound
∀[x:ℝ]. (x ≤ r((((x 1) + 1) ÷ 2) + 1))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
int-to-real: r(n),
real: ℝ,
uall: ∀[x:A]. B[x],
apply: f a,
divide: n ÷ m,
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat_plus: ℕ+,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False
Lemmas referenced :
real-upper-bound,
decidable__lt,
full-omega-unsat,
intformnot_wf,
intformless_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-less_than,
mul-commutes,
real_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality_alt,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
universeIsType
Latex:
\mforall{}[x:\mBbbR{}]. (x \mleq{} r((((x 1) + 1) \mdiv{} 2) + 1))
Date html generated:
2019_10_31-AM-06_10_43
Last ObjectModification:
2019_01_30-PM-02_03_09
Theory : reals_2
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