Nuprl Lemma : pointwise-rleq_wf
∀[n,m:ℤ]. ∀[x,y:{n..m + 1-} ⟶ ℝ]. (x[k] ≤ y[k] for k ∈ [n,m] ∈ ℙ)
Proof
Definitions occuring in Statement :
pointwise-rleq: x[k] ≤ y[k] for k ∈ [n,m],
real: ℝ,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
pointwise-rleq: x[k] ≤ y[k] for k ∈ [n,m],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
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],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
real_wf,
int_seg_wf,
lelt_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
rleq_wf,
le_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
lambdaEquality,
functionEquality,
hypothesisEquality,
hypothesis,
because_Cache,
applyEquality,
dependent_set_memberEquality,
independent_pairFormation,
dependent_functionElimination,
addEquality,
natural_numberEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n,m:\mBbbZ{}]. \mforall{}[x,y:\{n..m + 1\msupminus{}\} {}\mrightarrow{} \mBbbR{}]. (x[k] \mleq{} y[k] for k \mmember{} [n,m] \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-07_44_39
Last ObjectModification:
2016_01_17-AM-02_06_16
Theory : reals
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