Nuprl Lemma : rless_ibs_wf
∀[x,y:ℝ]. (rless_ibs(x;y) ∈ IBS)
Proof
Definitions occuring in Statement :
rless_ibs: rless_ibs(x;y),
incr-binary-seq: IBS,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rless_ibs: rless_ibs(x;y),
mkibs: mkibs(n.p[n]),
so_lambda: λ2x.t[x],
nat: ℕ,
real: ℝ,
nat_plus: ℕ+,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
so_apply: x[s],
l_exists: (∃x∈L. P[x]),
subtype_rel: A ⊆r B,
less_than': less_than'(a;b),
guard: {T},
uiff: uiff(P;Q),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
mkibs_wf,
bl-exists_wf,
int_seg_wf,
upto_wf,
lt_int_wf,
int_seg_properties,
nat_properties,
decidable__lt,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
istype-less_than,
l_member_wf,
istype-nat,
length_upto,
decidable__le,
istype-le,
length_wf,
select-upto,
select_wf,
add_nat_plus,
int_seg_subtype_nat,
istype-false,
nat_plus_properties,
add-is-int-iff,
intformeq_wf,
int_formula_prop_eq_lemma,
false_wf,
l_exists_wf,
less_than_wf,
assert-bl-exists,
l_exists_functionality,
assert_wf,
iff_weakening_uiff,
assert_of_lt_int,
istype-assert,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality_alt,
natural_numberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
applyEquality,
dependent_set_memberEquality_alt,
productElimination,
imageElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
setIsType,
lambdaFormation_alt,
productIsType,
inhabitedIsType,
closedConclusion,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
baseClosed,
equalityIstype
Latex:
\mforall{}[x,y:\mBbbR{}]. (rless\_ibs(x;y) \mmember{} IBS)
Date html generated:
2019_10_30-AM-10_15_53
Last ObjectModification:
2019_06_28-PM-01_55_43
Theory : real!vectors
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