Nuprl Lemma : imonomial-term-add
∀vs:ℤ List. ∀a,b:ℤ-o. ∀f:ℤ ⟶ ℤ. ((int_term_value(f;imonomial-term(<a, vs>)) + int_term_value(f;imonomial-term(<b, vs>)\000C)) = int_term_value(f;imonomial-term(<a + b, vs>)) ∈ ℤ)
Proof
Definitions occuring in Statement :
imonomial-term: imonomial-term(m),
int_term_value: int_term_value(f;t),
list: T List,
int_nzero: ℤ-o,
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
pair: <a, b>,
add: n + m,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
int_nzero: ℤ-o,
true: True,
subtype_rel: A ⊆r B,
top: Top,
squash: ↓T,
prop: ℙ,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
int_nzero_wf,
list_wf,
int_term_value_wf,
imonomial-term_wf,
mul-distributes-right,
equal_wf,
squash_wf,
true_wf,
add_functionality_wrt_eq,
imonomial-term-linear,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
functionEquality,
intEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionExtensionality,
applyEquality,
hypothesisEquality,
independent_pairEquality,
setElimination,
rename,
multiplyEquality,
because_Cache,
natural_numberEquality,
addEquality,
sqequalRule,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
independent_isectElimination,
dependent_functionElimination,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}vs:\mBbbZ{} List. \mforall{}a,b:\mBbbZ{}\msupminus{}\msupzero{}. \mforall{}f:\mBbbZ{} {}\mrightarrow{} \mBbbZ{}.
((int\_term\_value(f;imonomial-term(<a, vs>)) + int\_term\_value(f;imonomial-term(<b, vs>))) = int\_ter\000Cm\_value(f;imonomial-term(<a + b, vs>)))
Date html generated:
2017_04_14-AM-08_57_56
Last ObjectModification:
2017_02_27-PM-03_41_04
Theory : omega
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