Nuprl Lemma : rmaximum_wf
∀[n,m:ℤ]. ∀[x:{n..m + 1-} ⟶ ℝ]. (rmaximum(n;m;k.x[k]) ∈ ℝ) supposing n ≤ m
Proof
Definitions occuring in Statement :
rmaximum: rmaximum(n;m;k.x[k]),
real: ℝ,
int_seg: {i..j-},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
le: A ≤ B,
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
rmaximum: rmaximum(n;m;k.x[k]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
nat: ℕ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
so_apply: x[s],
int_seg: {i..j-},
lelt: i ≤ j < k,
guard: {T}
Lemmas referenced :
int_seg_wf,
int_seg_properties,
rmax_wf,
lelt_wf,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
itermAdd_wf,
intformless_wf,
decidable__lt,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
subtract_wf,
decidable__le,
real_wf,
primrec_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_set_memberEquality,
because_Cache,
dependent_functionElimination,
natural_numberEquality,
hypothesisEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
applyEquality,
addEquality,
setElimination,
rename,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[n,m:\mBbbZ{}]. \mforall{}[x:\{n..m + 1\msupminus{}\} {}\mrightarrow{} \mBbbR{}]. (rmaximum(n;m;k.x[k]) \mmember{} \mBbbR{}) supposing n \mleq{} m
Date html generated:
2016_05_18-AM-07_49_48
Last ObjectModification:
2016_01_17-AM-02_09_04
Theory : reals
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