Nuprl Lemma : normalize-constraint-eq
∀[k:ℕ]. ∀[A:ℕ ⟶ ℚ × ℤ]. (normalize-constraint(k;A) = A ∈ (ℕ ⟶ ℚ × ℤ))
Proof
Definitions occuring in Statement :
normalize-constraint: normalize-constraint(k;p),
rationals: ℚ,
nat: ℕ,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
normalize-constraint: normalize-constraint(k;p),
has-value: (a)↓,
uimplies: b supposing a,
nat: ℕ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
callbyvalueall: callbyvalueall,
has-valueall: has-valueall(a),
select?: as[i]?a,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
top: Top,
squash: ↓T,
int_seg: {i..j-},
lelt: i ≤ j < k,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x]
Lemmas referenced :
nat_wf,
rationals_wf,
value-type-has-value,
int-value-type,
valueall-type-has-valueall,
list_wf,
list-valueall-type,
rationals-valueall-type,
map_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
upto_wf,
evalall-reduce,
lt_int_wf,
length_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
less_than_wf,
le_int_wf,
le_wf,
bnot_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_lt_int,
assert_of_le_int,
equal_wf,
length-map,
squash_wf,
true_wf,
map_select,
lelt_wf,
iff_weakening_equal,
non_neg_length,
map_length,
nat_properties,
decidable__le,
select_wf,
length_wf_nat,
int_seg_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformnot_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
int_formula_prop_wf,
select_upto,
length_upto
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
productEquality,
functionEquality,
extract_by_obid,
thin,
intEquality,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
hypothesisEquality,
axiomEquality,
because_Cache,
productElimination,
callbyvalueReduce,
independent_isectElimination,
natural_numberEquality,
setElimination,
rename,
applyEquality,
lambdaEquality,
independent_pairFormation,
lambdaFormation,
independent_pairEquality,
functionExtensionality,
equalityTransitivity,
equalitySymmetry,
baseClosed,
unionElimination,
equalityElimination,
independent_functionElimination,
dependent_functionElimination,
voidElimination,
voidEquality,
imageElimination,
universeEquality,
dependent_set_memberEquality,
imageMemberEquality,
applyLambdaEquality,
dependent_pairFormation,
int_eqEquality,
computeAll
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[A:\mBbbN{} {}\mrightarrow{} \mBbbQ{} \mtimes{} \mBbbZ{}]. (normalize-constraint(k;A) = A)
Date html generated:
2018_05_22-AM-00_20_59
Last ObjectModification:
2017_07_26-PM-06_55_31
Theory : rationals
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