Nuprl Lemma : mkibs_wf
∀[p:ℕ ⟶ 𝔹]. mkibs(n.p[n]) ∈ IBS supposing ∀n:ℕ. ((↑p[n]) ⇒ (↑p[n + 1]))
Proof
Definitions occuring in Statement :
mkibs: mkibs(n.p[n]),
incr-binary-seq: IBS,
nat: ℕ,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
incr-binary-seq: IBS,
mkibs: mkibs(n.p[n]),
so_apply: x[s],
int_seg: {i..j-},
nat: ℕ,
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
le: A ≤ B,
less_than': less_than'(a;b),
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b
Lemmas referenced :
ifthenelse_wf,
int_seg_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-le,
istype-less_than,
istype-nat,
intformand_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
istype-assert,
bool_wf,
eqtt_to_assert,
istype-false,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
add-commutes,
assert_elim,
not_assert_elim,
btrue_neq_bfalse
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
hypothesisEquality,
natural_numberEquality,
hypothesis,
setElimination,
rename,
independent_pairFormation,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
universeIsType,
productIsType,
lambdaFormation_alt,
because_Cache,
functionIsType,
addEquality,
int_eqEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectIsTypeImplies,
inhabitedIsType,
equalityElimination,
productElimination,
equalityIstype,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}[p:\mBbbN{} {}\mrightarrow{} \mBbbB{}]. mkibs(n.p[n]) \mmember{} IBS supposing \mforall{}n:\mBbbN{}. ((\muparrow{}p[n]) {}\mRightarrow{} (\muparrow{}p[n + 1]))
Date html generated:
2019_10_30-AM-10_15_48
Last ObjectModification:
2019_06_28-PM-01_55_39
Theory : real!vectors
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