Nuprl Lemma : frs-increasing-non-dec
∀[p:ℝ List]. (frs-increasing(p) ⇒ frs-non-dec(p))
Proof
Definitions occuring in Statement :
frs-increasing: frs-increasing(p),
frs-non-dec: frs-non-dec(L),
real: ℝ,
list: T List,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
frs-increasing: frs-increasing(p),
frs-non-dec: frs-non-dec(L),
all: ∀x:A. B[x],
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
rless: x < y,
sq_exists: ∃x:{A| B[x]},
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
subtype_rel: A ⊆r B,
real: ℝ,
sq_stable: SqStable(P),
rleq: x ≤ y,
rnonneg: rnonneg(x),
le: A ≤ B
Lemmas referenced :
rleq_weakening_equal,
list_wf,
nat_plus_wf,
rsub_wf,
less_than'_wf,
frs-increasing_wf,
int_seg_wf,
le_wf,
int_term_value_constant_lemma,
itermConstant_wf,
decidable__le,
nat_plus_properties,
sq_stable__less_than,
select_wf,
rleq_weakening_rless,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
intformeq_wf,
itermVar_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
real_wf,
length_wf,
int_seg_properties,
int_subtype_base,
subtype_base_sq,
decidable__equal_int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
lemma_by_obid,
setElimination,
rename,
unionElimination,
instantiate,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
because_Cache,
independent_functionElimination,
natural_numberEquality,
productElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
addEquality,
applyEquality,
imageElimination,
imageMemberEquality,
baseClosed,
independent_pairEquality,
minusEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[p:\mBbbR{} List]. (frs-increasing(p) {}\mRightarrow{} frs-non-dec(p))
Date html generated:
2016_05_18-AM-08_53_09
Last ObjectModification:
2016_01_17-AM-02_29_42
Theory : reals
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