Nuprl Lemma : no-weak-limited-omniscience
¬(∀f:ℕ ⟶ 𝔹. Dec(∀n:ℕ. f n = ff))
Proof
Definitions occuring in Statement :
nat: ℕ,
bfalse: ff,
bool: 𝔹,
decidable: Dec(P),
all: ∀x:A. B[x],
not: ¬A,
apply: f a,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uiff: uiff(P;Q),
bfalse: ff,
ifthenelse: if b then t else f fi ,
assert: ↑b,
top: Top,
satisfiable_int_formula: satisfiable_int_formula(fmla),
ge: i ≥ j ,
lelt: i ≤ j < k,
int_seg: {i..j-},
nat: ℕ,
false: False,
rev_implies: P ⇐ Q,
guard: {T},
uimplies: b supposing a,
subtype_rel: A ⊆r B,
true: True,
and: P ∧ Q,
iff: P ⇐⇒ Q,
isl: isl(x),
exists: ∃x:A. B[x],
squash: ↓T,
or: P ∨ Q,
decidable: Dec(P),
all: ∀x:A. B[x],
weak-continuity: weak-continuity(T;V),
so_apply: x[s],
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
implies: P ⇒ Q,
not: ¬A
Lemmas referenced :
assert_of_bnot,
iff_weakening_uiff,
iff_transitivity,
bnot_wf,
eqff_to_assert,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
decidable__le,
false_wf,
assert_wf,
assert_of_lt_int,
less_than_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
intformless_wf,
intformand_wf,
full-omega-unsat,
nat_properties,
int_seg_properties,
iff_imp_equal_bool,
lt_int_wf,
iff_wf,
le_wf,
int_seg_wf,
btrue_neq_bfalse,
equal-wf-base,
iff_weakening_equal,
subtype_rel_self,
bfalse_wf,
true_wf,
squash_wf,
equal_wf,
not_wf,
isl_wf,
equal-wf-T-base,
decidable_wf,
bool_wf,
nat_wf,
all_wf,
weak-continuity-bool-bool
Rules used in proof :
addEquality,
impliesFunctionality,
addLevel,
voidEquality,
isect_memberEquality,
intEquality,
int_eqEquality,
approximateComputation,
dependent_set_memberEquality,
setElimination,
voidElimination,
independent_isectElimination,
instantiate,
imageMemberEquality,
natural_numberEquality,
universeEquality,
independent_pairFormation,
unionElimination,
dependent_pairFormation,
productElimination,
imageElimination,
independent_functionElimination,
equalitySymmetry,
equalityTransitivity,
because_Cache,
functionExtensionality,
dependent_functionElimination,
rename,
baseClosed,
hypothesisEquality,
applyEquality,
lambdaEquality,
sqequalRule,
functionEquality,
thin,
isectElimination,
sqequalHypSubstitution,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
hypothesis,
extract_by_obid,
introduction,
cut
Latex:
\mneg{}(\mforall{}f:\mBbbN{} {}\mrightarrow{} \mBbbB{}. Dec(\mforall{}n:\mBbbN{}. f n = ff))
Date html generated:
2018_07_29-AM-09_29_10
Last ObjectModification:
2018_07_27-PM-04_24_05
Theory : basic
Home
Index