Nuprl Lemma : ipolynomial-term-cons-value
∀[m:iMonomial()]. ∀[p:iMonomial() List].
∀f:ℤ ⟶ ℤ
(int_term_value(f;ipolynomial-term([m / p]))
= (int_term_value(f;imonomial-term(m)) + int_term_value(f;ipolynomial-term(p)))
∈ ℤ)
Proof
Definitions occuring in Statement :
ipolynomial-term: ipolynomial-term(p),
imonomial-term: imonomial-term(m),
iMonomial: iMonomial(),
int_term_value: int_term_value(f;t),
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
add: n + m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
equiv_int_terms: t1 ≡ t2,
uimplies: b supposing a,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
int_term_value: int_term_value(f;t),
itermAdd: left "+" right,
int_term_ind: int_term_ind,
iMonomial: iMonomial(),
int_nzero: ℤ-o
Lemmas referenced :
ipolynomial-term-cons,
subtype_base_sq,
int_subtype_base,
int_term_value_wf,
imonomial-term_wf,
ipolynomial-term_wf,
list_wf,
iMonomial_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
dependent_functionElimination,
instantiate,
cumulativity,
intEquality,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalRule,
addEquality,
productElimination,
independent_pairEquality,
setElimination,
rename,
because_Cache,
functionEquality
Latex:
\mforall{}[m:iMonomial()]. \mforall{}[p:iMonomial() List].
\mforall{}f:\mBbbZ{} {}\mrightarrow{} \mBbbZ{}
(int\_term\_value(f;ipolynomial-term([m / p]))
= (int\_term\_value(f;imonomial-term(m)) + int\_term\_value(f;ipolynomial-term(p))))
Date html generated:
2016_05_14-AM-07_01_00
Last ObjectModification:
2015_12_26-PM-01_11_44
Theory : omega
Home
Index