Nuprl Lemma : decidable__reducible
∀n:ℕ. Dec(reducible(n))
Proof
Definitions occuring in Statement :
reducible: reducible(a),
nat: ℕ,
decidable: Dec(P),
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
reducible: reducible(a),
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
so_lambda: λ2x.t[x],
int_nzero: ℤ-o,
so_apply: x[s],
rev_implies: P ⇐ Q,
int_seg: {i..j-},
gt: i > j,
nequal: a ≠ b ∈ T ,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
squash: ↓T,
subtype_rel: A ⊆r B,
true: True,
guard: {T},
nat_plus: ℕ+,
le: A ≤ B,
uiff: uiff(P;Q),
less_than': less_than'(a;b),
subtract: n - m,
divides: b | a,
lelt: i ≤ j < k,
cand: A c∧ B,
assoced: a ~ b,
sq_type: SQType(T)
Lemmas referenced :
nat_wf,
decidable__equal_int,
reducible_wf,
not_wf,
or_wf,
equal-wf-T-base,
exists_wf,
int_nzero_wf,
assoced_wf,
equal_wf,
int_seg_wf,
pos_mul_arg_bounds,
int_nzero_properties,
nat_properties,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermMultiply_wf,
itermVar_wf,
intformeq_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_mul_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
absval_wf,
absval_pos,
decidable__le,
le_wf,
iff_weakening_equal,
squash_wf,
true_wf,
absval_mul,
intformimplies_wf,
intformor_wf,
int_formual_prop_imp_lemma,
int_formula_prop_or_lemma,
divisors_bound,
false_wf,
not-lt-2,
not-equal-2,
add_functionality_wrt_le,
add-associates,
add-zero,
zero-add,
le-add-cancel,
condition-implies-le,
add-commutes,
minus-add,
minus-zero,
less_than_wf,
multiply-is-int-iff,
absval-non-neg,
itermAdd_wf,
int_term_value_add_lemma,
lelt_wf,
divides_of_absvals,
divides_wf,
subtype_base_sq,
int_subtype_base,
int_seg_properties,
nequal_wf,
decidable__or,
decidable__exists_int_seg,
decidable__and2,
decidable__not,
decidable__assoced,
decidable_functionality,
int_entire
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
extract_by_obid,
hypothesis,
rename,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
hypothesisEquality,
natural_numberEquality,
unionElimination,
inlFormation,
isectElimination,
because_Cache,
intEquality,
equalityTransitivity,
equalitySymmetry,
baseClosed,
independent_pairFormation,
productElimination,
sqequalRule,
lambdaEquality,
productEquality,
multiplyEquality,
addEquality,
independent_functionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
applyEquality,
imageElimination,
equalityUniverse,
levelHypothesis,
dependent_set_memberEquality,
imageMemberEquality,
universeEquality,
minusEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
applyLambdaEquality,
instantiate,
cumulativity,
orFunctionality,
inrFormation
Latex:
\mforall{}n:\mBbbN{}. Dec(reducible(n))
Date html generated:
2017_04_17-AM-09_42_44
Last ObjectModification:
2017_02_27-PM-05_38_03
Theory : num_thy_1
Home
Index