Nuprl Lemma : rsum-rewrite-test
Σ{r(i) | 1≤i≤10} ≤ Σ{r(1 + i) | 1≤i≤10}
Proof
Definitions occuring in Statement :
rsum: Σ{x[k] | n≤k≤m},
rleq: x ≤ y,
int-to-real: r(n),
add: n + m,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
decidable: Dec(P),
or: P ∨ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
so_apply: x[s],
rev_uimplies: rev_uimplies(P;Q),
rge: x ≥ y,
guard: {T}
Lemmas referenced :
rsum_functionality_wrt_rleq2,
rleq_functionality_wrt_implies,
rleq_weakening_equal,
le_wf,
int_seg_wf,
int-to-real_wf,
rsum_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformle_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__le,
rleq-int
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
addEquality,
natural_numberEquality,
productElimination,
independent_functionElimination,
because_Cache,
hypothesis,
unionElimination,
isectElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
setElimination,
rename
Latex:
\mSigma{}\{r(i) | 1\mleq{}i\mleq{}10\} \mleq{} \mSigma{}\{r(1 + i) | 1\mleq{}i\mleq{}10\}
Date html generated:
2016_05_18-AM-07_45_28
Last ObjectModification:
2016_01_17-AM-02_06_42
Theory : reals
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