Nuprl Lemma : rcos-seq-increasing
∀n:ℕ. (rcos-seq(n) < rcos-seq(n + 1))
Proof
Definitions occuring in Statement :
rcos-seq: rcos-seq(n),
rless: x < y,
nat: ℕ,
all: ∀x:A. B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
nat: ℕ,
rless: x < y,
sq_exists: ∃x:{A| B[x]},
subtype_rel: A ⊆r B,
real: ℝ,
sq_stable: SqStable(P),
implies: P ⇒ Q,
squash: ↓T,
nat_plus: ℕ+,
ge: i ≥ j ,
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,
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
guard: {T},
cand: A c∧ B
Lemmas referenced :
rcos-seq-positive,
nat_wf,
rcos-seq_wf,
sq_stable__less_than,
int-to-real_wf,
real_wf,
nat_plus_properties,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
le_wf,
radd_wf,
rcos_wf,
rless_functionality,
req_weakening,
rcos-seq-step,
radd-preserves-rless,
rminus_wf,
member_rccint_lemma,
rleq_weakening_rless,
rleq_weakening_equal,
rleq_wf,
rmul_wf,
rless_wf,
radd-zero-both,
rmul-zero-both,
radd_functionality,
rmul_functionality,
radd-int,
req_transitivity,
rminus-as-rmul,
req_inversion,
rmul-identity1,
rmul-distrib2,
radd-assoc
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
productElimination,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
applyEquality,
lambdaEquality,
sqequalRule,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
because_Cache,
productEquality,
minusEquality,
addLevel
Latex:
\mforall{}n:\mBbbN{}. (rcos-seq(n) < rcos-seq(n + 1))
Date html generated:
2016_10_26-PM-00_18_13
Last ObjectModification:
2016_09_12-PM-05_41_38
Theory : reals_2
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