Nuprl Lemma : lower-right-endpoint_wf
∀[a,b:ℝ]. ∀[n:ℕ+].  (lower-right-endpoint(a;b;n) ∈ ℝ)
Proof
Definitions occuring in Statement : 
lower-right-endpoint: lower-right-endpoint(a;b;n)
, 
real: ℝ
, 
nat_plus: ℕ+
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
lower-right-endpoint: lower-right-endpoint(a;b;n)
, 
int_nzero: ℤ-o
, 
nat_plus: ℕ+
, 
nequal: a ≠ b ∈ T 
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
all: ∀x:A. B[x]
, 
top: Top
, 
and: P ∧ Q
, 
prop: ℙ
Lemmas referenced : 
real_wf, 
nat_plus_wf, 
int-rmul_wf, 
radd_wf, 
nequal_wf, 
equal_wf, 
int_formula_prop_wf, 
int_formula_prop_less_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_term_value_add_lemma, 
int_formula_prop_eq_lemma, 
int_formula_prop_and_lemma, 
intformless_wf, 
itermConstant_wf, 
itermVar_wf, 
itermAdd_wf, 
intformeq_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
nat_plus_properties, 
int-rdiv_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
dependent_set_memberEquality, 
addEquality, 
setElimination, 
rename, 
hypothesisEquality, 
natural_numberEquality, 
hypothesis, 
lambdaFormation, 
independent_isectElimination, 
dependent_pairFormation, 
lambdaEquality, 
int_eqEquality, 
intEquality, 
dependent_functionElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
independent_pairFormation, 
computeAll, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
because_Cache
Latex:
\mforall{}[a,b:\mBbbR{}].  \mforall{}[n:\mBbbN{}\msupplus{}].    (lower-right-endpoint(a;b;n)  \mmember{}  \mBbbR{})
Date html generated:
2016_05_18-AM-08_38_06
Last ObjectModification:
2016_01_17-AM-02_23_02
Theory : reals
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