Nuprl Lemma : length-minus-polynom
∀[n:ℕ+]. ∀[p:polyform(n)]. (||minus-polynom(n;p)|| = ||p|| ∈ ℤ)
Proof
Definitions occuring in Statement :
minus-polynom: minus-polynom(n;p),
polyform: polyform(n),
length: ||as||,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
polyform: polyform(n),
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
prop: ℙ,
all: ∀x:A. B[x],
or: P ∨ Q,
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
btrue: tt,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
bfalse: ff,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
minus-polynom: minus-polynom(n;p),
nat: ℕ,
decidable: Dec(P)
Lemmas referenced :
polyform_wf,
nat_plus_subtype_nat,
nat_plus_wf,
eq_int_wf,
assert_wf,
bnot_wf,
not_wf,
equal-wf-T-base,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
nat_plus_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
subtract_wf,
decidable__le,
intformnot_wf,
intformle_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_subtract_lemma,
le_wf,
minus-polynom_wf,
polyform-value-type,
map_length,
map-rev-sq-map
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
hypothesis,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
setElimination,
rename,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
baseClosed,
dependent_functionElimination,
unionElimination,
instantiate,
cumulativity,
independent_isectElimination,
independent_functionElimination,
productElimination,
independent_pairFormation,
lambdaFormation,
impliesFunctionality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
voidElimination,
voidEquality,
computeAll,
int_eqReduceFalseSq,
dependent_set_memberEquality
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[p:polyform(n)]. (||minus-polynom(n;p)|| = ||p||)
Date html generated:
2017_09_29-PM-06_00_31
Last ObjectModification:
2017_05_03-PM-04_47_18
Theory : integer!polynomials
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